P Adic Analysis Arithmetic And Singularities

Author : Carlos Galindo
Publisher : American Mathematical Society
ISBN 13 : 1470467798
Total Pages : 311 pages
Book Rating : 4.91/5 ( download)

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Download or read book $p$-Adic Analysis, Arithmetic and Singularities written by Carlos Galindo and published by American Mathematical Society. This book was released on 2022-05-11 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :
ISBN 13 : 9781470469764
Total Pages : pages
Book Rating : 4.66/5 ( download)

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Download or read book P-adic Analysis, Arithmetic and Singularities written by Carlos Galindo and published by . This book was released on 2022 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Neal Koblitz
Publisher : Springer Science & Business Media
ISBN 13 :
Total Pages : 144 pages
Book Rating : 4.50/5 ( download)

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Download or read book P-adic Numbers, P-adic Analysis, and Zeta-functions written by Neal Koblitz and published by Springer Science & Business Media. This book was released on 1977 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Neal Koblitz
Publisher : Cambridge University Press
ISBN 13 : 0521280605
Total Pages : 171 pages
Book Rating : 4.00/5 ( download)

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Download or read book P-adic Analysis written by Neal Koblitz and published by Cambridge University Press. This book was released on 1980-11-28 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
ISBN 13 : 9780821884591
Total Pages : 172 pages
Book Rating : 4.9X/5 ( download)

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Download or read book P-adic Analysis Compared with Real written by Svetlana Katok and published by American Mathematical Soc.. This book was released on with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Svetlana Katok
Publisher :
ISBN 13 : 9780821852248
Total Pages : 152 pages
Book Rating : 4.48/5 ( download)

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Download or read book P-Adic Analysis Compared With Real, 1/e written by Svetlana Katok and published by . This book was released on 2007 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Alan Adolphson
Publisher : American Mathematical Soc.
ISBN 13 : 9780821854686
Total Pages : 260 pages
Book Rating : 4.82/5 ( download)

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Download or read book P-adic Methods in Number Theory and Algebraic Geometry written by Alan Adolphson and published by American Mathematical Soc.. This book was released on 1992-01-01 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two meetings of the AMS in the fall of 1989 included Special Sessions on the role of p-adic methods in number theory and algebraic geometry. This volume grew out of these Special Sessions. Drawn from a wide area of mathematics, the articles presented here provide an excellent sampling of the broad range of trends and applications in p&R-adic methods.

Author : Samuele Anni
Publisher : American Mathematical Society
ISBN 13 : 1470467941
Total Pages : 198 pages
Book Rating : 4.44/5 ( download)

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Download or read book Arithmetic, Geometry, Cryptography, and Coding Theory 2021 written by Samuele Anni and published by American Mathematical Society. This book was released on 2022-07-06 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Bernard Dwork
Publisher : Princeton University Press
ISBN 13 : 1400882540
Total Pages : 349 pages
Book Rating : 4.40/5 ( download)

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Download or read book An Introduction to G-Functions. (AM-133), Volume 133 written by Bernard Dwork and published by Princeton University Press. This book was released on 2016-03-02 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Hemen Dutta
Publisher : American Mathematical Society
ISBN 13 : 1470469642
Total Pages : 256 pages
Book Rating : 4.41/5 ( download)

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Download or read book Mathematical Modelling written by Hemen Dutta and published by American Mathematical Society. This book was released on 2023-06-12 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.