Analytic Methods In Arithmetic Geometry
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Analytic Methods In Arithmetic Geometry
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Author : Alina Bucur
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-11-22
Analytic Methods In Arithmetic Geometry written by Alina Bucur and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-22 with Education categories.
In the last decade or so, analytic methods have had great success in answering questions in arithmetic geometry and number theory. The School provided a unique opportunity to introduce graduate students to analytic methods in arithmetic geometry. The book contains four articles. Alina C. Cojocaru's article introduces sieving techniques to study the group structure of points of the reduction of an elliptic curve modulo a rational prime via its division fields. Harald A. Helfgott's article provides an introduction to the study of growth in groups of Lie type, with SL2(Fq) and some of its subgroups as the key examples. The article by Étienne Fouvry, Emmanuel Kowalski, Philippe Michel, and Will Sawin describes how a systematic use of the deep methods from ℓ-adic cohomology pioneered by Grothendieck and Deligne and further developed by Katz and Laumon help make progress on various classical questions from analytic number theory. The last article, by Andrew V. Sutherland, introduces Sato-Tate groups and explores their relationship with Galois representations, motivic L-functions, and Mumford-Tate groups.
Analytic Methods In Arithmetic Geometry
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Author : David Zureick-Brown
language : en
Publisher:
Release Date : 2019
Analytic Methods In Arithmetic Geometry written by David Zureick-Brown and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Arithmetical algebraic geometry categories.
This volume contains the proceedings of the Arizona Winter School 2016, which was held from March 12-16, 2016, at The University of Arizona, Tucson, AZ. In the last decade or so, analytic methods have had great success in answering questions in arithmetic geometry and number theory. The School provided a unique opportunity to introduce graduate students to analytic methods in arithmetic geometry. The book contains four articles. Alina C. Cojocaru's article introduces sieving techniques to study the group structure of points of the reduction of an elliptic curve modulo a rational prime via its division fields. Harald A. Helfgott's article provides an introduction to the study of growth in groups of Lie type, with \mathrmSL}_2(\mathbb{F}_q) and some of its subgroups as the key examples. The article by Étienne Fouvry, Emmanuel Kowalski, Philippe Michel, and Will Sawin describes how a systematic use of the deep methods from \ell-adic cohomology pioneered by Grothendieck and Deligne and further developed by Katz and Laumon help make progress on various classical questions from analytic number theory. The last article, by Andrew V. Sutherland, introduces Sato-Tate groups and explores their relationship with Galois representations, motivic L-functions, and Mumford-Tate groups.
Analytic Number Theory An Introductory Course
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Author : Paul Trevier Bateman
language : en
Publisher: World Scientific
Release Date : 2004-09-07
Analytic Number Theory An Introductory Course written by Paul Trevier Bateman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-07 with Mathematics categories.
This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative arithmetic functions. Both real variable (”elementary”) and complex variable (”analytic”) methods are employed. The reader is assumed to have knowledge of elementary number theory (abstract algebra will also do) and real and complex analysis. Specialized analytic techniques, including transform and Tauberian methods, are developed as needed.Comments and corrigenda for the book are found at www.math.uiuc.edu/~diamond/.
History Of Analytic Geometry
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Author : Carl B. Boyer
language : en
Publisher: Courier Corporation
Release Date : 2012-06-28
History Of Analytic Geometry written by Carl B. Boyer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-28 with Mathematics categories.
This study presents the concepts and contributions from before the Alexandrian Age through to Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850. 1956 edition. Analytical bibliography. Index.
Arithmetic Geometry And Number Theory
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Author : Lin Weng
language : en
Publisher: World Scientific
Release Date : 2006-06-02
Arithmetic Geometry And Number Theory written by Lin Weng and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-02 with Mathematics categories.
Mathematics is very much a part of our culture; and this invaluable collection serves the purpose of developing the branches involved, popularizing the existing theories and guiding our future explorations.More precisely, the goal is to bring the reader to the frontier of current developments in arithmetic geometry and number theory through the works of Deninger-Werner in vector bundles on curves over p-adic fields; of Jiang on local gamma factors in automorphic representations; of Weng on Deligne pairings and Takhtajan-Zograf metrics; of Yoshida on CM-periods; of Yu on transcendence of special values of zetas over finite fields. In addition, the lecture notes presented by Weng at the University of Toronto from October to November 2005 explain basic ideas and the reasons (not just the language and conclusions) behind Langlands' fundamental, yet notably difficult, works on the Eisenstein series and spectral decompositions.And finally, a brand new concept by Weng called the Geometric Arithmetic program that uses algebraic and/or analytic methods, based on geometric considerations, to develop the promising and yet to be cultivated land of global arithmetic that includes non-abelian Class Field Theory, Riemann Hypothesis and non-abelian Zeta and L Functions, etc.
New Complex Analytic Methods In The Study Of Non Orientable Minimal Surfaces In Rn
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Author : Antonio Alarcón
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-05-13
New Complex Analytic Methods In The Study Of Non Orientable Minimal Surfaces In Rn written by Antonio Alarcón and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-13 with Education categories.
All the new tools mentioned above apply to non-orientable minimal surfaces endowed with a fixed choice of a conformal structure. This enables the authors to obtain significant new applications to the global theory of non-orientable minimal surfaces. In particular, they construct proper non-orientable conformal minimal surfaces in Rn with any given conformal structure, complete non-orientable minimal surfaces in Rn with arbitrary conformal type whose generalized Gauss map is nondegenerate and omits n hyperplanes of CPn−1 in general position, complete non-orientable minimal surfaces bounded by Jordan curves, and complete proper non-orientable minimal surfaces normalized by bordered surfaces in p-convex domains of Rn.
Heights In Diophantine Geometry
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Author : Enrico Bombieri
language : en
Publisher: Cambridge University Press
Release Date : 2006
Heights In Diophantine Geometry written by Enrico Bombieri and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This monograph is a bridge between the classical theory and modern approach via arithmetic geometry.
Arithmetic Geometry
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Author : Clay Mathematics Institute. Summer School
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Arithmetic Geometry written by Clay Mathematics Institute. Summer School and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Based on survey lectures given at the 2006 Clay Summer School on Arithmetic Geometry at the Mathematics Institute of the University of Gottingen, this tile is intended for graduate students and recent PhD's. It introduces readers to modern techniques and conjectures at the interface of number theory and algebraic geometry.
Arithmetic Geometry Number Theory And Computation
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Author : Jennifer S. Balakrishnan
language : en
Publisher: Springer Nature
Release Date : 2022-03-15
Arithmetic Geometry Number Theory And Computation written by Jennifer S. Balakrishnan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-15 with Mathematics categories.
This volume contains articles related to the work of the Simons Collaboration “Arithmetic Geometry, Number Theory, and Computation.” The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces, and abelian varieties over number fields and finite fields. The articles also explore examples important for future research. Specific topics include● algebraic varieties over finite fields● the Chabauty-Coleman method● modular forms● rational points on curves of small genus● S-unit equations and integral points.
A Gyrovector Space Approach To Hyperbolic Geometry
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Author : Abraham A. Ungar
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2009
A Gyrovector Space Approach To Hyperbolic Geometry written by Abraham A. Ungar and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. The mission of this book is to open that door by making the hyperbolic geometry of Bolyai and Lobachevsky, as well as the special relativity theory of Einstein that it regulates, accessible to a wider audience in terms of novel analogies that the modern and unknown share with the classical and familiar. These novel analogies that this book captures stem from Thomas gyration, which is the mathematical abstraction of the relativistic effect known as Thomas precession. Remarkably, the mere introduction of Thomas gyration turns Euclidean geometry into hyperbolic geometry, and reveals mystique analogies that the two geometries share. Accordingly, Thomas gyration gives rise to the prefix "gyro" that is extensively used in the gyrolanguage of this book, giving rise to terms like gyrocommutative and gyroassociative binary operations in gyrogroups, and gyrovectors in gyrovector spaces. Of particular importance is the introduction of gyrovectors into hyperbolic geometry, where they are equivalence classes that add according to the gyroparallelogram law in full analogy with vectors, which are equivalence classes that add according to the parallelogram law. A gyroparallelogram, in turn, is a gyroquadrilateral the two gyrodiagonals of which intersect at their gyromidpoints in full analogy with a parallelogram, which is a quadrilateral the two diagonals of which intersect at their midpoints. Table of Contents: Gyrogroups / Gyrocommutative Gyrogroups / Gyrovector Spaces / Gyrotrigonometry