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Tuesday, May 19, 2020 | History

2 edition of On automorphic functions and the reciprocity law in a number field found in the catalog.

On automorphic functions and the reciprocity law in a number field

T. Kubota

On automorphic functions and the reciprocity law in a number field

by T. Kubota

  • 15 Want to read
  • 21 Currently reading

Published by Kinokuniya Book Store in Tokyo .
Written in English

    Subjects:
  • Automorphic functions.,
  • Eisenstein series.,
  • Representations of groups.

  • Edition Notes

    Statementby Tomio Kubota.
    SeriesLectures in mathematics - Dept. of Mathematics, Kyoto University ; 2
    The Physical Object
    Pagination65 p. :
    Number of Pages65
    ID Numbers
    Open LibraryOL22057238M

      After preliminaries--including a section, ``Notation and Terminology''--the first part of the book deals with automorphic forms on such groups. In particular, their rationality over a number field is defined and discussed in connection with the group action; also the reciprocity law for the values of automorphic functions at CM-points is : Goro Shimura. For a number field E, A Eis the ring of adeles of` Eand EOthe ring of finite ad`eles. We write A for A Q, A ffor QO, and A0for C A. The reciprocity law rec EWA E!=E/ is normalized so that a local uniformizing element maps to the inverse of the usual (number-theorists) Frobenius automorphism. Complex conjugation is denoted by or by a7.

    2 Arthur & Gelbart - Lectures on automorphic L-functions: Part I in which the reader can find further information. More detailed discussion is given in various parts of the Corvallis Proceedings and in many of the other references we have cited. PART I 1 STANDARD L-FUNCTIONS FOR GLn Let F be a fixed number field. ular functions of not too high level that can be used to produce class invarian ts. Proofs of all statemen ts in this section can be found in [4]. The basic example of a mo dular function is the j.

    Endoscopy Theory of Automorphic Forms 5 The Langlands conjectures. Let G be a reductive group over a global field F which can be a finite extension of Q or the field of rational functions of a smooth projective curve over a finite field. For each absolute value v on F, Fv denotes the completion of F with respect to v, and if v isCited by: 5. This is an easygoing study/discussion group to go over some books on automorphic forms and L-functions. We started by reading D. Bump's Automorphic Forms and Representations, published by Cambridge University Press.A learning seminar for Spring and Fall was primarily run by Lawrence Vu whose seminar webpage is here. If you want to participate or be on the mailing .


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On automorphic functions and the reciprocity law in a number field by T. Kubota Download PDF EPUB FB2

Get this from a library. On automorphic functions: and the reciprocity law in a number field. [T Kubota]. The Artin reciprocity law applies to a Galois extension of an algebraic number field whose Galois group is abelian; it assigns L-functions to the one-dimensional representations of this Galois group, and states that these L-functions are identical to certain Dirichlet L-series or more general series (that is, certain analogues of the Riemann.

This opened a field for later research on associated Dirichlet series and automorphic forms, and was a major step in the solution of Kummer's conjecture.

Works. On automorphic functions and the reciprocity law in a number field. Kinokuniya, Tokyo ; Notes on analytic theory of numbers. University of Chicago Press, Alma mater: Nagoya University (Ph.D.

After preliminaries—including a section, “Notation and Terminology”—the first part of the book deals with automorphic forms on such groups. In particular, their rationality over a number field is defined and discussed in connection with the group action; also the reciprocity law for the values of automorphic functions at CM-points is.

After preliminaries--including a section, "Notation and Terminology"--the first part of the book deals with automorphic forms on such groups. In particular, their rationality over a number field is defined and discussed in connection with the group action; also the reciprocity law for the values of automorphic functions at CM-points is proved.

The book features extensive foundational material on the representation theory of GL(1) and GL(2) over local fields, the theory of automorphic representations, L-functions and advanced topics such as the Langlands conjectures, the Weil representation, the Rankin–Selberg method and the triple L-function, examining this subject matter from many Cited by: Abstract.

The theory of automorphic forms of 1/2-integral weight has attracted a considerable amount of attention in recent years. The striking difference between the case of integral and 1/2-integral weight is the fact that the Fourier coefficients of 1/2-integral weight forms are expressible in terms of the values of by:   T.

Kubota, On automorphic functions and the reciprocity law in a number field, Lectures in Mathematics 2, Kyoto University, Google ScholarCited by: 6. The book features extensive foundational material on the representation theory of GL(1) and GL(2) over local fields, the theory of automorphic representations, L-functions and advanced topics such as the Langlands conjectures, the Weil representation, the Rankin-Selberg method and the triple L-function, and examines this subject matter from Cited by: The theta function proof is also discussed in Dym and McKean's book "Fourier Series and Integrals" and in Richard Bellman's book "A Brief Introduction to Theta Functions." Bellman points out that theta reciprocity is a remarkable consequence of the fact that when the theta function is extended to two variables, both sides of the.

You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.

This volume contains the proceedings of the workshop on “Advances in the Theory of Automorphic Forms and Their \(L\)-functions” held in honor of James Cogdell's 60th birthday, held from October 16–25,at the Erwin Schrödinger Institute (ESI) at. L-functions, the zeta-functions of Riemann and Dedekind, and the L-functions of Dirichlet, and begin with the more general functions introduced in this century by Hecke [19] and by Artin [2].

Artin’s reciprocity law is the pattern to which all others, born and unborn, are cut. After preliminaries--including a section, ``Notation and Terminology''--the first part of the book deals with automorphic forms on such groups.

In particular, their rationality over a number field is defined and discussed in connection with the group action; also the reciprocity law for the values of automorphic functions at CM-points is proved.

Get this from a library. Automorphic forms and Shimura varieties of PGSp (2). [Yuval Z Flicker] -- The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms.

A guiding principle is a reciprocity law relating. Modern Analysis of Automorphic Forms by Example [current version ] is my (page, in x 11 inches format) PDF version of the physical book, from Cambridge University Press, Cambridge Studies in Advanced Mathematics, volumes and Number Theory, Trace Formulas and Discrete Groups: Symposium in Honor of Atle Selberg Oslo, Norway, Julyis a collection of papers presented at the Selberg Symposium, held at the University of Oslo.

This symposium contains 30 lectures that cover the significant contribution of Atle Selberg in the field of mathematics. Goro Shimura’s monograph, Introduction to the Arithmetic Theory of Automorphic Functions, published originally by Iwanami Shoten together with Princeton University Press, and now re-issued in paperback by Princeton, is one of the most important books in the is also beautifully structured and very well-written, if compactly.

It is unimaginable. analysis, analytic number theory. Dihua Jiang Professor automorphic forms, L-functions, number theory, harmonic analysis, representation theory. Kai-Wen Lan Associate Professor number theory, automorphic forms, Shimura varieties and related topics in arithmetric geometry.

William Messing Professor. Fourier expansion of periodic adelic functions 23 Adelic Poisson summation formula 30 Exercises for Chapter 1 31 2 Automorphic representations and L-functions for GL(1,AQ)39 Automorphic forms for GL(1,AQ)39 The L-function of an automorphic form 45 The local L-functions and their functional equations.

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.

The area of automorphic representations is a natural continuation of studies in number theory and modular forms. A guiding principle is a reciprocity law relating the infinite dimensional automorphic representations with finite dimensional Galois representations.[KubotaBook] T.

Kubota, On Automorphic Functions and the Reciprocity Law in a Number Field, Tokyo: Kinokuniya Book-Store Co. Ltd.,vol. 2. Show bibtex @book Cited by: