Topic
Modular form
About: Modular form is a research topic. Over the lifetime, 6156 publications have been published within this topic receiving 115916 citations.
Papers published on a yearly basis
1 / 2
Papers
Book•
1 Jan 1971
TL;DR: The second edition of Lang's well-known textbook as mentioned in this paper contains a version of a Riemann-Roch theorem in number fields, proved by Lang in the very first version of the book in the sixties.
Abstract: This is a corrected printing of the second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cyclotomic fields, or modular forms. Part I introduces some of the basic ideas of the theory: number fields, ideal classes, ideles and adeles, and zeta functions. It also contains a version of a Riemann-Roch theorem in number fields, proved by Lang in the very first version of the book in the sixties. This version can now be seen as a precursor of Arakelov theory. Part II covers class field theory, and Part III is devoted to analytic methods, including an exposition of Tate's thesis, the Brauer-Siegel theorem, and Weil's explicit formulas. The second edition contains corrections, as well as several additions to the previous edition, and the last chapter on explicit formulas has been rewritten.
2,663 citations
Book•
1 Jan 1971
TL;DR: The cohomology group assoicated with cusp forms and arithmetic Fuschian groups of the first kind was introduced in this paper..., where we have shown that it is possible to construct an algebraic algebraic curve and a complex multiplication of elliptic curves.
Abstract: * uschian groups of the first kind * Automorphic forms and functions * Hecke operators and the zeta-functions associated with modular forms * Elliptic curves * Abelian extensions of imaginary quadratic fields and complex multiplication of elliptic curves * Modular functions of higher level * Zeta-functions of algebraic curves and abelian varieties * The cohomology group assoicated with cusp forms * Arithmetic Fuschian groups
1,386 citations
Book•
1 Jan 1976
TL;DR: The second volume of Mathematics 160 as mentioned in this paper is devoted to elliptic functions and modular functions with some of their number-theoretic applications, including Rademacher's convergent series for the partition function, Lehner's congruences for the Fourier coefficients of the modular functionj( r), and Hecke's theory of entire forms with multiplicative Fouriers coefficients.
Abstract: This is the second volume of a 2-volume textbook which evolved from a course (Mathematics 160) offered at the California Institute of Technology du ring the last 25 years The second volume presupposes a background in number theory com¬ parable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis Most of the present volume is devoted to elliptic functions and modular functions with some of their number-theoretic applications Among the major topics treated are Rademacher's convergent series for the partition function, Lehner's congruences for the Fourier coefficients of the modular functionj( r), and Hecke's theory of entire forms with multiplicative Fourier coefficients The last chapter gives an account of Bohr's theory of equivalence of general Dirichlet series Both volumes of this work emphasize classical aspects of a subject wh ich in recent years has undergone a great deal of modern development It is hoped that these volumes will help the nonspecialist become acquainted with an important and fascinating part of mathematics and, at the same time, will provide some of the background that belongs to the repertory of every specialist in the field This volume, like the first, is dedicated to the students who have taken this course and have gone on to make notable contributions to number theory and other parts of mathematics T M A January, 1976
1,308 citations
TL;DR: In this paper, the authors present conditions générales d'utilisation (http://www.numdam.org/conditions), i.e., Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
Abstract: © Publications mathématiques de l’I.H.É.S., 1977, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
1,275 citations
Book•
1 Jan 1984
TL;DR: The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory as discussed by the authors, and the current state of knowledge of ellipses.
Abstract: The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse-Weil L-function and the conjecture of Birch and Swinnerton-Dyer. The second edition of this text includes an updated bibliography indicating the latest, dramatic changes in the direction of proving the Birch and Swinnerton conjecture. It also discusses the current state of knowledge of elliptic curves.
1,200 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 63 |
| 2024 | 69 |
| 2023 | 257 |
| 2022 | 492 |
| 2021 | 315 |
| 2020 | 331 |