Introduction to the Arithmetic Theory of Automorphic Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to the Arithmetic Theory of Automorphic Functions write by Gorō Shimura. This book was released on 1971-08-21. Introduction to the Arithmetic Theory of Automorphic Functions available in PDF, EPUB and Kindle. The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular forms with emphasis on their number-theoretical aspects. After two chapters geared toward elementary levels, there follows a detailed treatment of the theory of Hecke operators, which associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian varieties is discussed. The main question is the construction of abelian extensions of certain algebraic number fields, which is traditionally called "Hilbert's twelfth problem." Another advanced topic is the determination of the zeta function of an algebraic curve uniformized by modular functions, which supplies an indispensable background for the recent proof of Fermat's last theorem by Wiles.
Automorphic Forms
Automorphic Forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Automorphic Forms write by Anton Deitmar. This book was released on 2012-08-29. Automorphic Forms available in PDF, EPUB and Kindle. Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem. This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essential aspects and restricting it to the 'base field' of rational numbers. Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic.
Introductory Lectures on Automorphic Forms
Introductory Lectures on Automorphic Forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introductory Lectures on Automorphic Forms write by Walter L. Baily Jr.. This book was released on 2015-03-08. Introductory Lectures on Automorphic Forms available in PDF, EPUB and Kindle. Intended as an introductory guide, this work takes for its subject complex, analytic, automorphic forms and functions on (a domain equivalent to) a bounded domain in a finite-dimensional, complex, vector space, usually denoted Cn). Part I, essentially elementary, deals with complex analytic automorphic forms on a bounded domain; it presents H. Cartan's proof of the existence of the projective imbedding of the compact quotient of such a domain by a discrete group. Part II treats the construction and properties of automorphic forms with respect to an arithmetic group acting on a bounded symmetric domain; this part is highly technical, and based largely on relevant results in functional analysis due to Godement and Harish-Chandra. In Part III, Professor Baily extends the discussion to include some special topics, specifically, the arithmetic propertics of Eisenstein series and their connection with the arithmetic theory of quadratic forms. Unlike classical works on the subject, this book deals with more than one variable, and it differs notably in its treatment of analysis on the group of automorphisms of the domain. It is concerned with the case of complex analytic automorphic forms because of their connection with algebraic geometry, and so is distinct from other modern treatises that deal with automorphic forms on a semi-simple Lie group. Having had its inception as graduate- level lectures, the book assumes some knowledge of complex function theory and algebra, for the serious reader is expected to supply certain details for himself, especially in such related areas as functional analysis and algebraic groups. Originally published in 1973. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Abelian Varieties with Complex Multiplication and Modular Functions
Abelian Varieties with Complex Multiplication and Modular Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Abelian Varieties with Complex Multiplication and Modular Functions write by Goro Shimura. This book was released on 2016-06-02. Abelian Varieties with Complex Multiplication and Modular Functions available in PDF, EPUB and Kindle. Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential functions. A similar theory can be developed for special values of elliptic or elliptic modular functions, and is called complex multiplication of such functions. In 1900 Hilbert proposed the generalization of these as the twelfth of his famous problems. In this book, Goro Shimura provides the most comprehensive generalizations of this type by stating several reciprocity laws in terms of abelian varieties, theta functions, and modular functions of several variables, including Siegel modular functions. This subject is closely connected with the zeta function of an abelian variety, which is also covered as a main theme in the book. The third topic explored by Shimura is the various algebraic relations among the periods of abelian integrals. The investigation of such algebraicity is relatively new, but has attracted the interest of increasingly many researchers. Many of the topics discussed in this book have not been covered before. In particular, this is the first book in which the topics of various algebraic relations among the periods of abelian integrals, as well as the special values of theta and Siegel modular functions, are treated extensively.
Automorphic Forms on GL (3,TR)
Automorphic Forms on GL (3,TR) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Automorphic Forms on GL (3,TR) write by D. Bump. This book was released on 2006-12-08. Automorphic Forms on GL (3,TR) available in PDF, EPUB and Kindle.
