Problems In The Theory Of Modular Forms
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Problems In The Theory Of Modular Forms
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Author : M. Ram Murty
language : en
Publisher: Springer
Release Date : 2016-11-25
Problems In The Theory Of Modular Forms written by M. Ram Murty and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-25 with Mathematics categories.
This book introduces the reader to the fascinating world of modular forms through a problem-solving approach. As such, besides researchers, the book can be used by the undergraduate and graduate students for self-instruction. The topics covered include q-series, the modular group, the upper half-plane, modular forms of level one and higher level, the Ramanujan τ-function, the Petersson inner product, Hecke operators, Dirichlet series attached to modular forms and further special topics. It can be viewed as a gentle introduction for a deeper study of the subject. Thus, it is ideal for non-experts seeking an entry into the field.
Some Applications Of Modular Forms
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Author : Peter Sarnak
language : en
Publisher: Cambridge University Press
Release Date : 1990-11-15
Some Applications Of Modular Forms written by Peter Sarnak 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 1990-11-15 with Mathematics categories.
The theory of modular forms and especially the so-called 'Ramanujan Conjectures' have been applied to resolve problems in combinatorics, computer science, analysis and number theory. This tract, based on the Wittemore Lectures given at Yale University, is concerned with describing some of these applications. In order to keep the presentation reasonably self-contained, Professor Sarnak begins by developing the necessary background material in modular forms. He then considers the solution of three problems: the Ruziewicz problem concerning finitely additive rotationally invariant measures on the sphere; the explicit construction of highly connected but sparse graphs: 'expander graphs' and 'Ramanujan graphs'; and the Linnik problem concerning the distribution of integers that represent a given large integer as a sum of three squares. These applications are carried out in detail. The book therefore should be accessible to a wide audience of graduate students and researchers in mathematics and computer science.
Modular Forms And Functions
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Author : Robert A. Rankin
language : en
Publisher: Cambridge University Press
Release Date : 2008-12-04
Modular Forms And Functions written by Robert A. Rankin 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 2008-12-04 with Mathematics categories.
This book provides an introduction to the theory of elliptic modular functions and forms, a subject of increasing interest because of its connexions with the theory of elliptic curves. Modular forms are generalisations of functions like theta functions. They can be expressed as Fourier series, and the Fourier coefficients frequently possess multiplicative properties which lead to a correspondence between modular forms and Dirichlet series having Euler products. The Fourier coefficients also arise in certain representational problems in the theory of numbers, for example in the study of the number of ways in which a positive integer may be expressed as a sum of a given number of squares. The treatment of the theory presented here is fuller than is customary in a textbook on automorphic or modular forms, since it is not confined solely to modular forms of integral weight (dimension). It will be of interest to professional mathematicians as well as senior undergraduate and graduate students in pure mathematics.
The Congruence Subgroup Problem An Elementary Approach Aimed At Applications
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Author : B. Sury
language : en
Publisher: Springer
Release Date : 2003-01-01
The Congruence Subgroup Problem An Elementary Approach Aimed At Applications written by B. Sury and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
Computational Aspects Of Modular Forms And Elliptic Curves
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Author : Dennis Charles
language : en
Publisher:
Release Date : 2005
Computational Aspects Of Modular Forms And Elliptic Curves written by Dennis Charles and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Sums Of Squares Of Integers
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Author : Carlos J. Moreno
language : en
Publisher: CRC Press
Release Date : 2005-12-09
Sums Of Squares Of Integers written by Carlos J. Moreno and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-09 with Mathematics categories.
Sums of Squares of Integers covers topics in combinatorial number theory as they relate to counting representations of integers as sums of a certain number of squares. The book introduces a stimulating area of number theory where research continues to proliferate. It is a book of "firsts" - namely it is the first book to combine Liouville's elementary methods with the analytic methods of modular functions to study the representation of integers as sums of squares. It is the first book to tell how to compute the number of representations of an integer n as the sum of s squares of integers for any s and n. It is also the first book to give a proof of Szemeredi's theorem, and is the first number theory book to discuss how the modern theory of modular forms complements and clarifies the classical fundamental results about sums of squares. The book presents several existing, yet still interesting and instructive, examples of modular forms. Two chapters develop useful properties of the Bernoulli numbers and illustrate arithmetic progressions, proving the theorems of van der Waerden, Roth, and Szemeredi. The book also explains applications of the theory to three problems that lie outside of number theory in the areas of cryptanalysis, microwave radiation, and diamond cutting. The text is complemented by the inclusion of over one hundred exercises to test the reader's understanding.
The 1 2 3 Of Modular Forms
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Author : Jan Hendrik Bruinier
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-10
The 1 2 3 Of Modular Forms written by Jan Hendrik Bruinier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-10 with Mathematics categories.
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.
Discrete Mathematics And Graph Theory
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Author : Dr. Jhade Srinivas
language : en
Publisher: RK Publication
Release Date : 2024-11-13
Discrete Mathematics And Graph Theory written by Dr. Jhade Srinivas and has been published by RK Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-13 with Mathematics categories.
Discrete Mathematics and Graph Theory the foundational concepts and advanced topics of discrete mathematics and graph theory. Designed for students and professionals in mathematics, computer science, and engineering, it explores topics like logic, set theory, combinatorics, graph algorithms, and network flows. The emphasizes problem-solving, rigorous proofs, and real-world applications, making it an essential resource for mastering discrete structures and their role in computational and theoretical disciplines. With clear explanations and numerous examples, it bridges the gap between theory and practice effectively.
Nine Mathematical Challenges An Elucidation
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Author : A. Kechris
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-09-24
Nine Mathematical Challenges An Elucidation written by A. Kechris 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 2021-09-24 with Education categories.
This volume stems from the Linde Hall Inaugural Math Symposium, held from February 22–24, 2019, at California Institute of Technology, Pasadena, California. The content isolates and discusses nine mathematical problems, or sets of problems, in a deep way, but starting from scratch. Included among them are the well-known problems of the classification of finite groups, the Navier-Stokes equations, the Birch and Swinnerton-Dyer conjecture, and the continuum hypothesis. The other five problems, also of substantial importance, concern the Lieb–Thirring inequalities, the equidistribution problems in number theory, surface bundles, ramification in covers and curves, and the gap and type problems in Fourier analysis. The problems are explained succinctly, with a discussion of what is known and an elucidation of the outstanding issues. An attempt is made to appeal to a wide audience, both in terms of the field of expertise and the level of the reader.
Fields Medallists Lectures 2nd Edition
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Author : Michael Atiyah
language : en
Publisher: World Scientific
Release Date : 2003-11-03
Fields Medallists Lectures 2nd Edition written by Michael Atiyah and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-03 with Mathematics categories.
Although the Fields Medal does not have the same public recognition as the Nobel Prizes, they share a similar intellectual standing. It is restricted to one field — that of mathematics — and an age limit of 40 has become an accepted tradition. Mathematics has in the main been interpreted as pure mathematics, and this is not so unreasonable since major contributions in some applied areas can be (and have been) recognized with Nobel Prizes.A list of Fields Medallists and their contributions provides a bird's-eye view of mathematics over the past 60 years. It highlights the areas in which, at various times, greatest progress has been made. This volume does not pretend to be comprehensive, nor is it a historical document. On the other hand, it presents contributions from Fields Medallists and so provides a highly interesting and varied picture.The second edition of Fields Medallists' Lectures features additional contributions from the following Medallists: Kunihiko Kodaira (1954), Richard E Borcherds (1998), William T Gowers (1998), Maxim Kontsevich (1998), Curtis T McMullen (1998) and Vladimir Voevodsky (2002).