On Dwork S P Adic Formal Congruences Theorem And Hypergeometric Mirror Maps

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On Dwork's $p$-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps

E. Delaygue,T. Rivoal,J. Roques
On Dwork s p Adic Formal Congruences Theorem and Hypergeometric Mirror Maps Book PDF

Author : E. Delaygue,T. Rivoal,J. Roques
Publisher : American Mathematical Soc.
Page : 94 pages
File Size : 54,8 Mb
Release : 2017-02-20
Category : Congruences (Geometry)
ISBN : 9781470423001

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On Dwork's $p$-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps by E. Delaygue,T. Rivoal,J. Roques Pdf

Using Dwork's theory, the authors prove a broad generalization of his famous -adic formal congruences theorem. This enables them to prove certain -adic congruences for the generalized hypergeometric series with rational parameters; in particular, they hold for any prime number and not only for almost all primes. Furthermore, using Christol's functions, the authors provide an explicit formula for the “Eisenstein constant” of any hypergeometric series with rational parameters. As an application of these results, the authors obtain an arithmetic statement “on average” of a new type concerning the integrality of Taylor coefficients of the associated mirror maps. It contains all the similar univariate integrality results in the literature, with the exception of certain refinements that hold only in very particular cases.

Harmonic Maass Forms and Mock Modular Forms: Theory and Applications

Kathrin Bringmann,Amanda Folsom,Ken Ono,Larry Rolen
Harmonic Maass Forms and Mock Modular Forms Theory and Applications Book PDF

Author : Kathrin Bringmann,Amanda Folsom,Ken Ono,Larry Rolen
Publisher : American Mathematical Soc.
Page : 391 pages
File Size : 47,8 Mb
Release : 2017-12-15
Category : Forms (Mathematics)
ISBN : 9781470419448

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Harmonic Maass Forms and Mock Modular Forms: Theory and Applications by Kathrin Bringmann,Amanda Folsom,Ken Ono,Larry Rolen Pdf

Modular forms and Jacobi forms play a central role in many areas of mathematics. Over the last 10–15 years, this theory has been extended to certain non-holomorphic functions, the so-called “harmonic Maass forms”. The first glimpses of this theory appeared in Ramanujan's enigmatic last letter to G. H. Hardy written from his deathbed. Ramanujan discovered functions he called “mock theta functions” which over eighty years later were recognized as pieces of harmonic Maass forms. This book contains the essential features of the theory of harmonic Maass forms and mock modular forms, together with a wide variety of applications to algebraic number theory, combinatorics, elliptic curves, mathematical physics, quantum modular forms, and representation theory.

The 1-2-3 of Modular Forms

Jan Hendrik Bruinier,Gerard van der Geer,Günter Harder,Don Zagier
The 1 2 3 of Modular Forms Book PDF

Author : Jan Hendrik Bruinier,Gerard van der Geer,Günter Harder,Don Zagier
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 54,5 Mb
Release : 2008-02-10
Category : Mathematics
ISBN : 9783540741190

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The 1-2-3 of Modular Forms by Jan Hendrik Bruinier,Gerard van der Geer,Günter Harder,Don Zagier Pdf

This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.

Mirror Symmetry II

Brian Greene,Shing-Tung Yau
Mirror Symmetry II Book PDF

Author : Brian Greene,Shing-Tung Yau
Publisher : American Mathematical Soc.
Page : 862 pages
File Size : 53,7 Mb
Release : 1997
Category : Conformal invariants
ISBN : 9780821827444

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Mirror Symmetry II by Brian Greene,Shing-Tung Yau Pdf

Mirror Symmetry has undergone dramatic progress since the Mathematical Sciences Research Institute (MSRI) workshop in 1991, whose proceedings constitute voluem I of this continuing collection. Tremendous insight has been gained on a number of key issues. This volume surveys these results. Some of the contributions in this work have appeared elsewhere, while others were written specifically for this collection. The areas covered are organized into 4 sections, and each presents papers by both physicists and mathematicians. This volume collects the most important developments that have taken place in mathematical physics since 1991. It is an essential reference tool for both mathematics and physics libraries and for students of physics and mathematics. Titles in this series are co-published, between the American Mathematical Society and International Press, Cambridge, MA, USA.

Symmetric Functions and Hall Polynomials

Ian Grant Macdonald
Symmetric Functions and Hall Polynomials Book PDF

Author : Ian Grant Macdonald
Publisher : Oxford University Press
Page : 496 pages
File Size : 55,8 Mb
Release : 1998
Category : Mathematics
ISBN : 0198504500

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Symmetric Functions and Hall Polynomials by Ian Grant Macdonald Pdf

This reissued classic text is the acclaimed second edition of Professor Ian Macdonald's groundbreaking monograph on symmetric functions and Hall polynomials. The first edition was published in 1979, before being significantly expanded into the present edition in 1995. This text is widely regarded as the best source of information on Hall polynomials and what have come to be known as Macdonald polynomials, central to a number of key developments in mathematics and mathematical physics in the 21st century Macdonald polynomials gave rise to the subject of double affine Hecke algebras (or Cherednik algebras) important in representation theory. String theorists use Macdonald polynomials to attack the so-called AGT conjectures. Macdonald polynomials have been recently used to construct knot invariants. They are also a central tool for a theory of integrable stochastic models that have found a number of applications in probability, such as random matrices, directed polymers in random media, driven lattice gases, and so on. Macdonald polynomials have become a part of basic material that a researcher simply must know if (s)he wants to work in one of the above domains, ensuring this new edition will appeal to a very broad mathematical audience. Featuring a new foreword by Professor Richard Stanley of MIT.

Algebra, Arithmetic, and Geometry

Yuri Tschinkel,Yuri Zarhin
Algebra Arithmetic and Geometry Book PDF

Author : Yuri Tschinkel,Yuri Zarhin
Publisher : Springer Science & Business Media
Page : 700 pages
File Size : 46,9 Mb
Release : 2010-04-11
Category : Mathematics
ISBN : 9780817647476

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Algebra, Arithmetic, and Geometry by Yuri Tschinkel,Yuri Zarhin Pdf

EMAlgebra, Arithmetic, and Geometry: In Honor of Yu. I. ManinEM consists of invited expository and research articles on new developments arising from Manin’s outstanding contributions to mathematics.

Exponential Sums and Differential Equations. (AM-124), Volume 124

Nicholas M. Katz
Exponential Sums and Differential Equations AM 124 Volume 124 Book PDF

Author : Nicholas M. Katz
Publisher : Princeton University Press
Page : 445 pages
File Size : 44,5 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882434

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Exponential Sums and Differential Equations. (AM-124), Volume 124 by Nicholas M. Katz Pdf

This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with polynomial coefficients, and the theory of one parameter families of exponential sums over finite fields. After reviewing some results from representation theory, the book discusses results about differential equations and their differential galois groups (G) and one-parameter families of exponential sums and their geometric monodromy groups (G). The final part of the book is devoted to comparison theorems relating G and G of suitably "corresponding" situations, which provide a systematic explanation of the remarkable "coincidences" found "by hand" in the hypergeometric case.

Modular And Automorphic Forms & Beyond

Hossein Movasati
Modular And Automorphic Forms Beyond Book PDF

Author : Hossein Movasati
Publisher : World Scientific
Page : 323 pages
File Size : 47,6 Mb
Release : 2021-10-12
Category : Mathematics
ISBN : 9789811238697

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Modular And Automorphic Forms & Beyond by Hossein Movasati Pdf

The guiding principle in this monograph is to develop a new theory of modular forms which encompasses most of the available theory of modular forms in the literature, such as those for congruence groups, Siegel and Hilbert modular forms, many types of automorphic forms on Hermitian symmetric domains, Calabi-Yau modular forms, with its examples such as Yukawa couplings and topological string partition functions, and even go beyond all these cases. Its main ingredient is the so-called 'Gauss-Manin connection in disguise'.

Black Holes in Higher Dimensions

Gary T. Horowitz
Black Holes in Higher Dimensions Book PDF

Author : Gary T. Horowitz
Publisher : Cambridge University Press
Page : 437 pages
File Size : 54,5 Mb
Release : 2012-04-19
Category : Science
ISBN : 9781107013452

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Black Holes in Higher Dimensions by Gary T. Horowitz Pdf

The first book devoted to black holes in more than four dimensions, for graduate students and researchers.

Lectures on Algebraic Statistics

Mathias Drton,Bernd Sturmfels,Seth Sullivant
Lectures on Algebraic Statistics Book PDF

Author : Mathias Drton,Bernd Sturmfels,Seth Sullivant
Publisher : Springer Science & Business Media
Page : 172 pages
File Size : 55,5 Mb
Release : 2009-04-25
Category : Mathematics
ISBN : 9783764389055

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Lectures on Algebraic Statistics by Mathias Drton,Bernd Sturmfels,Seth Sullivant Pdf

How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semi-algebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models.

The Maple Book

Frank Garvan
The Maple Book Book PDF

Author : Frank Garvan
Publisher : CRC Press
Page : 494 pages
File Size : 44,8 Mb
Release : 2001-11-28
Category : Mathematics
ISBN : 9781420035605

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The Maple Book by Frank Garvan Pdf

Maple is a very powerful computer algebra system used by students, educators, mathematicians, statisticians, scientists, and engineers for doing numerical and symbolic computations. Greatly expanded and updated from the author's MAPLE V Primer, The MAPLE Book offers extensive coverage of the latest version of this outstanding software package, MAPL

Proceedings of the International Congress of Mathematicians

S.D. Chatterji
Proceedings of the International Congress of Mathematicians Book PDF

Author : S.D. Chatterji
Publisher : Birkhäuser
Page : 1669 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034890786

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Proceedings of the International Congress of Mathematicians by S.D. Chatterji Pdf

Since the first ICM was held in Zürich in 1897, it has become the pinnacle of mathematical gatherings. It aims at giving an overview of the current state of different branches of mathematics and its applications as well as an insight into the treatment of special problems of exceptional importance. The proceedings of the ICMs have provided a rich chronology of mathematical development in all its branches and a unique documentation of contemporary research. They form an indispensable part of every mathematical library. The Proceedings of the International Congress of Mathematicians 1994, held in Zürich from August 3rd to 11th, 1994, are published in two volumes. Volume I contains an account of the organization of the Congress, the list of ordinary members, the reports on the work of the Fields Medalists and the Nevanlinna Prize Winner, the plenary one-hour addresses, and the invited addresses presented at Section Meetings 1 - 6. Volume II contains the invited address for Section Meetings 7 - 19. A complete author index is included in both volumes. '...the content of these impressive two volumes sheds a certain light on the present state of mathematical sciences and anybody doing research in mathematics should look carefully at these Proceedings. For young people beginning research, this is even more important, so these are a must for any serious mathematics library. The graphical presentation is, as always with Birkhäuser, excellent....' (Revue Roumaine de Mathematiques pures et Appliquées)

My Search for Ramanujan

Ken Ono,Amir D. Aczel
My Search for Ramanujan Book PDF

Author : Ken Ono,Amir D. Aczel
Publisher : Springer
Page : 238 pages
File Size : 42,5 Mb
Release : 2016-04-20
Category : Mathematics
ISBN : 9783319255682

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My Search for Ramanujan by Ken Ono,Amir D. Aczel Pdf

"The son of a prominent Japanese mathematician who came to the United States after World War II, Ken Ono was raised on a diet of high expectations and little praise. Rebelling against his pressure-cooker of a life, Ken determined to drop out of high school to follow his own path. To obtain his father’s approval, he invoked the biography of the famous Indian mathematical prodigy Srinivasa Ramanujan, whom his father revered, who had twice flunked out of college because of his single-minded devotion to mathematics. Ono describes his rocky path through college and graduate school, interweaving Ramanujan’s story with his own and telling how at key moments, he was inspired by Ramanujan and guided by mentors who encouraged him to pursue his interest in exploring Ramanujan’s mathematical legacy. Picking up where others left off, beginning with the great English mathematician G.H. Hardy, who brought Ramanujan to Cambridge in 1914, Ono has devoted his mathematical career to understanding how in his short life, Ramanujan was able to discover so many deep mathematical truths, which Ramanujan believed had been sent to him as visions from a Hindu goddess. And it was Ramanujan who was ultimately the source of reconciliation between Ono and his parents. Ono’s search for Ramanujan ranges over three continents and crosses paths with mathematicians whose lives span the globe and the entire twentieth century and beyond. Along the way, Ken made many fascinating discoveries. The most important and surprising one of all was his own humanity."

Computational Mathematics with SageMath

P. Zimmermann,A. Casamayou,N. Cohen,G. Connan,T. Dumont,L. Fousse,F. Maltey,M. Meulien,M. Mezzarobba,C. Pernet,N. M. Thi?ry,E. Bray,J. Cremona,M. Forets,A. Ghitza,H. Thomas
Computational Mathematics with SageMath Book PDF

Author : P. Zimmermann,A. Casamayou,N. Cohen,G. Connan,T. Dumont,L. Fousse,F. Maltey,M. Meulien,M. Mezzarobba,C. Pernet,N. M. Thi?ry,E. Bray,J. Cremona,M. Forets,A. Ghitza,H. Thomas
Publisher : SIAM
Page : 459 pages
File Size : 48,5 Mb
Release : 2018-12-10
Category : Science
ISBN : 9781611975451

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Computational Mathematics with SageMath by P. Zimmermann,A. Casamayou,N. Cohen,G. Connan,T. Dumont,L. Fousse,F. Maltey,M. Meulien,M. Mezzarobba,C. Pernet,N. M. Thi?ry,E. Bray,J. Cremona,M. Forets,A. Ghitza,H. Thomas Pdf

This fantastic and deep book about how to use Sage for learning and doing mathematics at all levels perfectly complements the existing Sage documentation. It is filled with many carefully thought through examples and exercises, and great care has been taken to put computational functionality into proper mathematical context. Flip to almost any random page in this amazing book, and you will learn how to play with and visualize some beautiful part of mathematics. --- William A. Stein, CEO, SageMath, and professor of mathematics, University of Washington SageMath, or Sage for short, is an open-source mathematical software system based on the Python language and developed by an international community comprising hundreds of teachers and researchers, whose aim is to provide an alternative to the commercial products Magma, Maple, Mathematica, and MATLAB. To achieve this, Sage relies on many open-source programs, including GAP, Maxima, PARI, and various scientific libraries for Python, to which thousands of new functions have been added. Sage is freely available and is supported by all modern operating systems. Sage provides a wonderful scientific and graphical calculator for high school students, and it efficiently supports undergraduates in their computations in analysis, linear algebra, calculus, etc. For graduate students, researchers, and engineers in various mathematical specialties, Sage provides the most recent algorithms and tools, which is why several universities around the world already use Sage at the undergraduate level.

Noncommutative Geometry, Quantum Fields and Motives

Alain Connes,Matilde Marcolli
Noncommutative Geometry Quantum Fields and Motives Book PDF

Author : Alain Connes,Matilde Marcolli
Publisher : American Mathematical Soc.
Page : 785 pages
File Size : 49,7 Mb
Release : 2019-03-13
Category : Electronic
ISBN : 9781470450458

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Noncommutative Geometry, Quantum Fields and Motives by Alain Connes,Matilde Marcolli Pdf

The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.