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Lectures on Modular Forms

1962-03-21 Education
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Release : 1962-03-21
Genre : Education
Kind : eBook
Book Rating : 950/5 ( reviews)

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Book Synopsis Lectures on Modular Forms by : Robert C. Gunning

Download or read book Lectures on Modular Forms written by Robert C. Gunning. This book was released on 1962-03-21. Available in PDF, EPUB and Kindle. Book excerpt: New interest in modular forms of one complex variable has been caused chiefly by the work of Selberg and of Eichler. But there has been no introductory work covering the background of these developments. H. C. Gunning's book surveys techniques and problems; only the simpler cases are treated-modular forms of even weights without multipliers, the principal congruence subgroups, and the Hecke operators for the full modular group alone.

Introduction to Modular Forms

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 472/5 ( reviews)

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Book Synopsis Introduction to Modular Forms by : Serge Lang

Download or read book Introduction to Modular Forms written by Serge Lang. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This book gives a thorough introduction to several theories that are fundamental to research on modular forms. Most of the material, despite its importance, had previously been unavailable in textbook form. Complete and readable proofs are given... In conclusion, this book is a welcome addition to the literature for the growing number of students and mathematicians in other fields who want to understand the recent developments in the theory of modular forms." #Mathematical Reviews# "This book will certainly be indispensable to all those wishing to get an up-to-date initiation to the theory of modular forms." #Publicationes Mathematicae#

The 1-2-3 of Modular Forms

2008-02-10 Mathematics
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Release : 2008-02-10
Genre : Mathematics
Kind : eBook
Book Rating : 194/5 ( reviews)

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Book Synopsis The 1-2-3 of Modular Forms by : Jan Hendrik Bruinier

Download or read book The 1-2-3 of Modular Forms written by Jan Hendrik Bruinier. This book was released on 2008-02-10. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on Hilbert Modular Varieties and Modular Forms

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 95X/5 ( reviews)

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Book Synopsis Lectures on Hilbert Modular Varieties and Modular Forms by : Eyal Zvi Goren

Download or read book Lectures on Hilbert Modular Varieties and Modular Forms written by Eyal Zvi Goren. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to certain aspects of the theory of $p$-adic Hilbert modular forms and moduli spaces of abelian varieties with real multiplication. The theory of $p$-adic modular forms is presented first in the elliptic case, introducing the reader to key ideas of N. M. Katz and J.-P. Serre. It is re-interpreted from a geometric point of view, which is developed to present the rudiments of a similar theory for Hilbert modular forms. The theory of moduli spaces of abelianvarieties with real multiplication is presented first very explicitly over the complex numbers. Aspects of the general theory are then exposed, in particular, local deformation theory of abelian varieties in positive characteristic. The arithmetic of $p$-adic Hilbert modular forms and the geometry ofmoduli spaces of abelian varieties are related. This relation is used to study $q$-expansions of Hilbert modular forms, on the one hand, and stratifications of moduli spaces on the other hand. The book is addressed to graduate students and non-experts. It attempts to provide the necessary background to all concepts exposed in it. It may serve as a textbook for an advanced graduate course.

Introductory Lectures on Siegel Modular Forms

1990-02-23 Mathematics
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Release : 1990-02-23
Genre : Mathematics
Kind : eBook
Book Rating : 522/5 ( reviews)

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Book Synopsis Introductory Lectures on Siegel Modular Forms by : Helmut Klingen

Download or read book Introductory Lectures on Siegel Modular Forms written by Helmut Klingen. This book was released on 1990-02-23. Available in PDF, EPUB and Kindle. Book excerpt: From their inception, Siegel modular forms have been studied extensively because of their significance in both automorphic functions in several complex variables and number theory. The comprehensive theory of automorphic forms to subgroups of algebraic groups and the arithmetical theory of modular forms illustrate these two aspects in an illuminating manner. The author's aim is to present a straightforward and easily accessible survey of the main ideas of the theory at an elementary level, providing a sound basis from which the reader can study advanced works and undertake original research. This book is based on lectures given by the author for a number of years and is intended for a one-semester graduate course, though it can also be used profitably for self-study. The only prerequisites are a basic knowledge of algebra, number theory and complex analysis.

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