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Tuesday, May 5, 2020 | History

4 edition of Modular forms and Dirichlet series. found in the catalog.

Modular forms and Dirichlet series.

Andrew Ogg

Modular forms and Dirichlet series.

by Andrew Ogg

  • 155 Want to read
  • 0 Currently reading

Published by W. A. Benjamin in New York .
Written in English

    Subjects:
  • Forms, Modular.,
  • Modular functions.,
  • Dirichlet series.

  • Edition Notes

    Includes bibliography.

    SeriesMathematics lecture note series
    Classifications
    LC ClassificationsQA244 .O3
    The Physical Object
    Pagination1 v. (various pagings)
    ID Numbers
    Open LibraryOL5685188M
    LC Control Number69017031

    Among the major topics covered are Rademacher's convergent series for the partition modular function, Lehner's congruences for the Fourier coefficients of the modular function j, 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.   Free Online Library: Hecke's theory of modular forms and Dirichlet series.(Brief Article, Book Review) by "SciTech Book News"; Publishing industry Library and information science Science and technology, general.

    Read "Introduction to Siegel Modular Forms and Dirichlet Series" by Anatoli Andrianov available from Rakuten Kobo. Several years ago I was invited to an American university to give one-term graduate course on Siegel modular forms, Heck Brand: Springer New York. By Andrew Ogg: pp. xv, Cloth £s.6d., Paper £s. (W.A. Benjamin, Inc., New York, ).Author: Joseph Lehner.

    Apostol, Modular functions and Dirichlet series in number theory: another analytic number theory text, but this one is rooted in old-school analytic number theory. Ogg, Modular forms and Dirichlet series: an older text that consequently provides a di erent take on some things. 3File Size: KB. Also, Serre's course in arithmetic has something (chapter VII) on Modular Forms. And Shimura's Elementary Dirichlet Series and Modular Forms is of more managable size than (D-S), but assumes more familiarity with algebraic number theory than Serre.


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Modular forms and Dirichlet series by Andrew Ogg Download PDF EPUB FB2

The book will be of interest to graduate students and researchers who are interested in special values of L-functions, class number formulae, arithmetic properties of modular forms (especially their values), and the arithmetic properties of Dirichlet by: From the reviews: "Introduction to Siegel Modular Forms and Dirichlet Series is a compact but masterful presentation of this important generalization of the classical theory, and a good deal more.

beneficiaries of this wonderful book are the obvious candidates: students of number theory with their qualifying examinations behind them, or very gifted undergraduates who have Cited by: In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth theory of modular forms therefore belongs to complex analysis but the main importance of the theory has traditionally been in its connections with.

Siegel's Modular Forms and Dirichlet Series Course Given at the University of Maryland, – Search within book. Front Modular forms and Dirichlet series. book. Pages I-V. PDF. Preliminary remarks on topological groups.

Dirichlet series corresponding to modular forms. 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. Get this from a library. Elementary Dirichlet series and modular forms. [Gorō Shimura] -- "The main topics of this book are the critical values of Dirichlet L-functions and Hecke L-functions of an imaginary quadratic field, and various problems on elliptic modular forms."--Jacket.

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. Additional Physical Format: Online version: Ogg, Andrew. Modular forms and Dirichlet series. New York, W.A. Benjamin, (OCoLC) Material Type.

The two subjects, Dirichlet series and modular forms, are traditional subjects, but here they are treated in both orthodox and unorthodox ways. Regardless of the unorthodox treatment, the author has made the book accessible to those who are not familiar with such topics by including plenty of expository : $ Modular forms and Dirichlet series | Ogg A.

| download | B–OK. Download books for free. Find books. Part of the Progress in Mathematics book series (PM, volume ) Abstract. It was Ramanujan who in a fundamental paper of introduced his τ-function as the Fourier coefficient of a modular form and then attached a Dirichlet series to it.

Construction and arithmetical application of modular forms of low weight, in: () Modular Author: M. Ram Murty, V. Kumar Murty. 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.

Modular Functions and Dirichlet Series in Number Theory book. Read 2 reviews from the world's largest community for readers. A new edition of a classical /5. Siegel's Modular Forms and Dirichlet Series by Hans Maas,available at Book Depository with free delivery worldwide. modular forms using Dirichlet characters, and then explain how to compute a basis of Hecke eigenforms for each subspace using several approaches.

We also discuss congruences between modular forms and bounds needed to provably generate the Hecke algebra. Chapter 10 is about computing analytic invariants of modular Size: 2MB. Elementary Dirichlet series and modular forms Goro Shimura.

The main topics of the book are the critical values of Dirichlet L-functions and Hecke L-functions of an imaginary quadratic field, and various problems on elliptic modular forms. As to the values of Dirichlet L-functions, all previous papers and books reiterate a single old result. Hecke’s Theory of Modular Forms and Dirichlet Series will be of huge importance to fledgling number theorists working on modular forms — in fact, given Hecke’s exalted place in this part of the firmament, the book is really indispensable.

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.

Inat the Institute for Advanced Study, E Hecke gave a series of lectures on his theory of correspondence between modular forms and Dirichlet series. Since then, the Hecke correspondence has remained an active feature of number theory and, indeed, it is more important today than it was Price: $ Buy Elementary Dirichlet Series and Modular Forms (Springer Monographs in Mathematics) by Shimura, Goro (ISBN: ) from Amazon's Book Store.

Everyday low prices and free delivery on eligible s: 1. The two subjects, Dirichlet series and modular forms, are traditional subjects, but here they are treated in both orthodox and unorthodox ways. Regardless of the unorthodox treatment, the author has made the book accessible to those who are not familiar with such topics by including plenty of expository material.

Inat the Institute for Advanced Study, E Hecke gave a series of lectures on his theory of correspondence between modular forms and Dirichlet series. Since then, the Hecke correspondence has remained an active feature of number theory and, indeed, it is more important today than it was in So it is that Introduction to Siegel Modular Forms and Dirichlet Series is a compact but masterful presentation of this important generalization of the classical theory, and a good deal more.

Andrianov describes the book as “a concise but basically complete and self-contained introduction to the multiplicative theory of Siegel modular forms.