Spectral Methods Of Automorphic Forms PDF Download
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Author | : Henryk Iwaniec |
Publisher | : American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain |
Total Pages | : 220 |
Release | : 2021-11-17 |
Genre | : Mathematics |
ISBN | : 1470466228 |
Download Spectral Methods of Automorphic Forms Book in PDF, ePub and Kindle
Automorphic forms are one of the central topics of analytic number theory. In fact, they sit at the confluence of analysis, algebra, geometry, and number theory. In this book, Henryk Iwaniec once again displays his penetrating insight, powerful analytic techniques, and lucid writing style. The first edition of this book was an underground classic, both as a textbook and as a respected source for results, ideas, and references. Iwaniec treats the spectral theory of automorphic forms as the study of the space of $L^2$ functions on the upper half plane modulo a discrete subgroup. Key topics include Eisenstein series, estimates of Fourier coefficients, Kloosterman sums, the Selberg trace formula and the theory of small eigenvalues. Henryk Iwaniec was awarded the 2002 Cole Prize for his fundamental contributions to number theory.
Author | : Henryk Iwaniec |
Publisher | : |
Total Pages | : 272 |
Release | : 1995 |
Genre | : Automorphic forms |
ISBN | : |
Download Introduction to the Spectral Theory of Automorphic Forms Book in PDF, ePub and Kindle
Author | : |
Publisher | : |
Total Pages | : 96 |
Release | : 2011 |
Genre | : |
ISBN | : |
Download Some Applications of the Spectral Theory of Automorphic Forms Book in PDF, ePub and Kindle
Author | : Andreas Strömbergsson |
Publisher | : |
Total Pages | : 226 |
Release | : 2001 |
Genre | : Differential operators |
ISBN | : 9789150614565 |
Download Studies in the Analytic and Spectral Theory of Automorphic Forms Book in PDF, ePub and Kindle
Author | : A. B. Venkov |
Publisher | : American Mathematical Soc. |
Total Pages | : 196 |
Release | : 1983 |
Genre | : Mathematics |
ISBN | : 9780821830789 |
Download Spectral Theory of Automorphic Functions Book in PDF, ePub and Kindle
Author | : Roelof W. Bruggeman |
Publisher | : Springer Science & Business Media |
Total Pages | : 320 |
Release | : 2010-02-28 |
Genre | : Mathematics |
ISBN | : 3034603363 |
Download Families of Automorphic Forms Book in PDF, ePub and Kindle
Automorphic forms on the upper half plane have been studied for a long time. Most attention has gone to the holomorphic automorphic forms, with numerous applications to number theory. Maass, [34], started a systematic study of real analytic automorphic forms. He extended Hecke’s relation between automorphic forms and Dirichlet series to real analytic automorphic forms. The names Selberg and Roelcke are connected to the spectral theory of real analytic automorphic forms, see, e. g. , [50], [51]. This culminates in the trace formula of Selberg, see, e. g. , Hejhal, [21]. Automorphicformsarefunctionsontheupperhalfplanewithaspecialtra- formation behavior under a discontinuous group of non-euclidean motions in the upper half plane. One may ask how automorphic forms change if one perturbs this group of motions. This question is discussed by, e. g. , Hejhal, [22], and Phillips and Sarnak, [46]. Hejhal also discusses the e?ect of variation of the multiplier s- tem (a function on the discontinuous group that occurs in the description of the transformation behavior of automorphic forms). In [5]–[7] I considered variation of automorphic forms for the full modular group under perturbation of the m- tiplier system. A method based on ideas of Colin de Verdi` ere, [11], [12], gave the meromorphic continuation of Eisenstein and Poincar ́ e series as functions of the eigenvalue and the multiplier system jointly. The present study arose from a plan to extend these results to much more general groups (discrete co?nite subgroups of SL (R)).
Author | : A.B. Venkov |
Publisher | : Springer Science & Business Media |
Total Pages | : 189 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9400918925 |
Download Spectral Theory of Automorphic Functions Book in PDF, ePub and Kindle
'Et moi ..., si j'avait su comment en revcnrr, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back. Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Author | : Colette Moeglin |
Publisher | : Cambridge University Press |
Total Pages | : 382 |
Release | : 1995-11-02 |
Genre | : Mathematics |
ISBN | : 9780521418935 |
Download Spectral Decomposition and Eisenstein Series Book in PDF, ePub and Kindle
A self-contained introduction to automorphic forms, and Eisenstein series and pseudo-series, proving some of Langlands' work at the intersection of number theory and group theory.
Author | : D. Bump |
Publisher | : Springer |
Total Pages | : 196 |
Release | : 2006-12-08 |
Genre | : Mathematics |
ISBN | : 3540390553 |
Download Automorphic Forms on GL (3,TR) Book in PDF, ePub and Kindle
Author | : Ze-Li Dou |
Publisher | : Springer Science & Business Media |
Total Pages | : 131 |
Release | : 2012-12-15 |
Genre | : Mathematics |
ISBN | : 3642287085 |
Download Six Short Chapters on Automorphic Forms and L-functions Book in PDF, ePub and Kindle
"Six Short Chapters on Automorphic Forms and L-functions" treats the period conjectures of Shimura and the moment conjecture. These conjectures are of central importance in contemporary number theory, but have hitherto remained little discussed in expository form. The book is divided into six short and relatively independent chapters, each with its own theme, and presents a motivated and lively account of the main topics, providing professionals an overall view of the conjectures and providing researchers intending to specialize in the area a guide to the relevant literature. Ze-Li Dou and Qiao Zhang are both associate professors of Mathematics at Texas Christian University, USA.