P Adic Analysis Arithmetic And Singularities

Author : Carlos Galindo,Alejandro Melle Hernández,Julio José Moyano-Fernández,Wilson A. Zúñiga-Galindo
Publisher : American Mathematical Society
Page : 311 pages
File Size : 53,7 Mb
Release : 2022-05-11
Category : Mathematics
ISBN : 9781470467791

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$p$-Adic Analysis, Arithmetic and Singularities by Carlos Galindo,Alejandro Melle Hernández,Julio José Moyano-Fernández,Wilson A. Zúñiga-Galindo Pdf

This volume contains the proceedings of the 2019 Lluís A. Santaló Summer School on $p$-Adic Analysis, Arithmetic and Singularities, which was held from June 24–28, 2019, at the Universidad Internacional Menéndez Pelayo, Santander, Spain. The main purpose of the book is to present and analyze different incarnations of the local zeta functions and their multiple connections in mathematics and theoretical physics. Local zeta functions are ubiquitous objects in mathematics and theoretical physics. At the mathematical level, local zeta functions contain geometry and arithmetic information about the set of zeros defined by a finite number of polynomials. In terms of applications in theoretical physics, these functions play a central role in the regularization of Feynman amplitudes and Koba-Nielsen-type string amplitudes, among other applications. This volume provides a gentle introduction to a very active area of research that lies at the intersection of number theory, $p$-adic analysis, algebraic geometry, singularity theory, and theoretical physics. Specifically, the book introduces $p$-adic analysis, the theory of Archimedean, $p$-adic, and motivic zeta functions, singularities of plane curves and their Poincaré series, among other similar topics. It also contains original contributions in the aforementioned areas written by renowned specialists. This book is an important reference for students and experts who want to delve quickly into the area of local zeta functions and their many connections in mathematics and theoretical physics.

Author : Carlos Galindo
Publisher : Unknown
Page : 128 pages
File Size : 55,9 Mb
Release : 2022
Category : p-adic analysis
ISBN : 1470469766

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P-adic Analysis, Arithmetic and Singularities by Carlos Galindo Pdf

Author : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 144 pages
File Size : 51,8 Mb
Release : 1977
Category : Mathematics
ISBN : UOM:39015015604450

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P-adic Numbers, P-adic Analysis, and Zeta-functions by Neal Koblitz Pdf

Author : Neal Koblitz
Publisher : Cambridge University Press
Page : 171 pages
File Size : 51,7 Mb
Release : 1980-11-28
Category : Mathematics
ISBN : 9780521280600

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P-adic Analysis by Neal Koblitz Pdf

An introduction to recent work in the theory of numbers and its interrelation with algebraic geometry and analysis.

Author : Svetlana Katok
Publisher : American Mathematical Soc.
Page : 152 pages
File Size : 54,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821842201

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P-adic Analysis Compared with Real by Svetlana Katok Pdf

The book gives an introduction to $p$-adic numbers from the point of view of number theory, topology, and analysis. Compared to other books on the subject, its novelty is both a particularly balanced approach to these three points of view and an emphasis on topics accessible to undergraduates. In addition, several topics from real analysis and elementary topology which are not usually covered in undergraduate courses (totally disconnected spaces and Cantor sets, points of discontinuity of maps and the Baire Category Theorem, surjectivity of isometries of compact metric spaces) are also included in the book. They will enhance the reader's understanding of real analysis and intertwine the real and $p$-adic contexts of the book. The book is based on an advanced undergraduate course given by the author. The choice of the topic was motivated by the internal beauty of the subject of $p$-adic analysis, an unusual one in the undergraduate curriculum, and abundant opportunities to compare it with its much more familiar real counterpart. The book includes a large number of exercises. Answers, hints, and solutions for most of them appear at the end of the book. Well written, with obvious care for the reader, the book can be successfully used in a topic course or for self-study.

Author : M. Ram Murty
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 53,7 Mb
Release : 2009-02-09
Category : Electronic
ISBN : 9780821888308

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Introduction to $P$-Adic Analytic Number Theory by M. Ram Murty Pdf

Historical introduction Bernoulli numbers $p$-adic numbers Hensel's lemma $p$-adic interpolation $p$-adic $L$-functions $p$-adic integration Leopoldt's formula for $L_p(1,\chi)$ Newton polygons An introduction to Iwasawa theory Bibliography Index

Author : Maruti Ram Murty
Publisher : Unknown
Page : 149 pages
File Size : 42,9 Mb
Release : 2002
Category : Number theory
ISBN : 1470417421

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Introduction to $p$-adic Analytic Number Theory by Maruti Ram Murty Pdf

This book is an elementary introduction to p-adic analysis from the number theory perspective. With over 100 exercises included, it will acquaint the non-expert to the basic ideas of the theory and encourage the novice to enter this fertile field of research. The main focus of the book is the study of p-adic L-functions and their analytic properties. It begins with a basic introduction to Bernoulli numbers and continues with establishing the Kummer congruences. These congruences are then used to construct the p-adic analog of the Riemann zeta function and p-adic analogs of Dirichlet's L-functi.

Author : Svetlana Katok,Svetlana
Publisher : Unknown
Page : 152 pages
File Size : 46,6 Mb
Release : 2007
Category : Electronic
ISBN : 0821852248

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P-Adic Analysis Compared With Real, 1/e by Svetlana Katok,Svetlana Pdf

Author : Bernard Dwork,Giovanni Gerotto,Francis J. Sullivan
Publisher : Princeton University Press
Page : 349 pages
File Size : 48,6 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882540

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An Introduction to G-Functions. (AM-133), Volume 133 by Bernard Dwork,Giovanni Gerotto,Francis J. Sullivan Pdf

Written for advanced undergraduate and first-year graduate students, this book aims to introduce students to a serious level of p-adic analysis with important implications for number theory. The main object is the study of G-series, that is, power series y=aij=0 Ajxj with coefficients in an algebraic number field K. These series satisfy a linear differential equation Ly=0 with LIK(x) [d/dx] and have non-zero radii of convergence for each imbedding of K into the complex numbers. They have the further property that the common denominators of the first s coefficients go to infinity geometrically with the index s. After presenting a review of valuation theory and elementary p-adic analysis together with an application to the congruence zeta function, this book offers a detailed study of the p-adic properties of formal power series solutions of linear differential equations. In particular, the p-adic radii of convergence and the p-adic growth of coefficients are studied. Recent work of Christol, Bombieri, André, and Dwork is treated and augmented. The book concludes with Chudnovsky's theorem: the analytic continuation of a G -series is again a G -series. This book will be indispensable for those wishing to study the work of Bombieri and André on global relations and for the study of the arithmetic properties of solutions of ordinary differential equations.

Author : W.H. Schikhof,C. Perez-Garcia,Jerzy Kakol
Publisher : CRC Press
Page : 416 pages
File Size : 54,9 Mb
Release : 2020-11-25
Category : Mathematics
ISBN : 9781000110067

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p-adic Functional Analysis by W.H. Schikhof,C. Perez-Garcia,Jerzy Kakol Pdf

"Contains research articles by nearly 40 leading mathematicians from North and South America, Europe, Africa, and Asia, presented at the Fourth International Conference on p-adic Functional Analysis held recently in Nijmegen, The Netherlands. Includes numerous new open problems documented with extensive comments and references."

Author : Samuele Anni,Valentijn Karemaker,Elisa Lorenzo García
Publisher : American Mathematical Society
Page : 198 pages
File Size : 48,7 Mb
Release : 2022-07-06
Category : Mathematics
ISBN : 9781470467944

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Arithmetic, Geometry, Cryptography, and Coding Theory 2021 by Samuele Anni,Valentijn Karemaker,Elisa Lorenzo García Pdf

This volume contains the proceedings of the 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, held (online) from May 31 to June 4, 2021. For over thirty years, the biennial international conference AGC$^2$T (Arithmetic, Geometry, Cryptography, and Coding Theory) has brought researchers together to forge connections between arithmetic geometry and its applications to coding theory and to cryptography. The papers illustrate the fruitful interaction between abstract theory and explicit computations, covering a large range of topics, including Belyi maps, Galois representations attached to elliptic curves, reconstruction of curves from their Jacobians, isogeny graphs of abelian varieties, hypergeometric equations, and Drinfeld modules.

Author : Bart Bories,Willem Veys
Publisher : American Mathematical Soc.
Page : 131 pages
File Size : 40,6 Mb
Release : 2016-06-21
Category : Functions, Zeta
ISBN : 9781470418410

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Igusa's $p$-Adic Local Zeta Function and the Monodromy Conjecture for Non-Degenerate Surface Singularities by Bart Bories,Willem Veys Pdf

In 2011 Lemahieu and Van Proeyen proved the Monodromy Conjecture for the local topological zeta function of a non-degenerate surface singularity. The authors start from their work and obtain the same result for Igusa's p-adic and the motivic zeta function. In the p-adic case, this is, for a polynomial f∈Z[x,y,z] satisfying f(0,0,0)=0 and non-degenerate with respect to its Newton polyhedron, we show that every pole of the local p-adic zeta function of f induces an eigenvalue of the local monodromy of f at some point of f−1(0)⊂C3 close to the origin. Essentially the entire paper is dedicated to proving that, for f as above, certain candidate poles of Igusa's p-adic zeta function of f, arising from so-called B1-facets of the Newton polyhedron of f, are actually not poles. This turns out to be much harder than in the topological setting. The combinatorial proof is preceded by a study of the integral points in three-dimensional fundamental parallelepipeds. Together with the work of Lemahieu and Van Proeyen, this main result leads to the Monodromy Conjecture for the p-adic and motivic zeta function of a non-degenerate surface singularity.

Author : A.K. Katsaras,W.H. Schikhof,L. Van Hamme
Publisher : CRC Press
Page : 337 pages
File Size : 49,9 Mb
Release : 2001-07-03
Category : Mathematics
ISBN : 9780203908143

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P-Adic Functional Analysis by A.K. Katsaras,W.H. Schikhof,L. Van Hamme Pdf

This volume collects together lectures presented at the Sixth International Conference held at the University of Ioannina, Greece, on p-adic functional analysis with applications in the fields of physics, differential equations, number theory, probability theory, dynamical systems, and algebraic number fields. It discusses the commutation relation AB-BA=I and its central role in quantum mechanics.

Author : Hemen Dutta
Publisher : American Mathematical Society
Page : 256 pages
File Size : 54,8 Mb
Release : 2023-06-12
Category : Mathematics
ISBN : 9781470469641

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Mathematical Modelling by Hemen Dutta Pdf

This volume is a collection of chapters that present several key principles and theories, as well as their potential uses in the development of mathematical models in areas like waves, thermodynamic, electromagnetics, fluid dynamics, and catastrophes. The techniques and methodologies used in this book, on the other hand, should have a long-term impact and be applicable to a wide range of different topics of study and research. Each chapter should also help readers in gaining a better knowledge of the underlying and connected concepts. The companion volume (Contemporary Mathematics, Volume 787) is devoted to theory and application.

Author : Bernard Dwork,Giovanni Gerotto,Francis J. Sullivan
Publisher : Princeton University Press
Page : 348 pages
File Size : 51,7 Mb
Release : 1994-05-22
Category : Mathematics
ISBN : 9780691036816

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An Introduction to G-functions by Bernard Dwork,Giovanni Gerotto,Francis J. Sullivan Pdf

After presenting a review of valuation theory and elementary p-adic analysis together with an application to the congruence zeta function, this book offers a detailed study of the p-adic properties of formal power series solutions of linear differential equations. In particular, the p-adic radii of convergence and the p-adic growth of coefficients are studied. Recent work of Christol, Bombieri, André, and Dwork is treated and augmented. The book concludes with Chudnovsky's theorem: the analytic continuation of a G -series is again a G -series. This book will be indispensable for those wishing to study the work of Bombieri and André on global relations and for the study of the arithmetic properties of solutions of ordinary differential equations.