Eisenstein Series Via the Poincaré Bundle and Applications
Author: Johannes Sprang
Publisher:
Published: 2017
Total Pages:
ISBN-13:
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Author: Johannes Sprang
Publisher:
Published: 2017
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAuthor: Philipp Fleig
Publisher: Cambridge University Press
Published: 2018-07-05
Total Pages: 588
ISBN-13: 1108118992
DOWNLOAD EBOOKThis introduction to automorphic forms on adelic groups G(A) emphasises the role of representation theory. The exposition is driven by examples, and collects and extends many results scattered throughout the literature, in particular the Langlands constant term formula for Eisenstein series on G(A) as well as the Casselman–Shalika formula for the p-adic spherical Whittaker function. This book also covers more advanced topics such as spherical Hecke algebras and automorphic L-functions. Many of these mathematical results have natural interpretations in string theory, and so some basic concepts of string theory are introduced with an emphasis on connections with automorphic forms. Throughout the book special attention is paid to small automorphic representations, which are of particular importance in string theory but are also of independent mathematical interest. Numerous open questions and conjectures, partially motivated by physics, are included to prompt the reader's own research.
Author: Helmut Klingen
Publisher:
Published: 1984
Total Pages: 18
ISBN-13:
DOWNLOAD EBOOKAuthor: Philipp Fleig
Publisher: Cambridge Studies in Advanced
Published: 2018-07-05
Total Pages: 587
ISBN-13: 1107189926
DOWNLOAD EBOOKDetailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.
Author: William A. Stein
Publisher: American Mathematical Soc.
Published: 2007-02-13
Total Pages: 290
ISBN-13: 0821839608
DOWNLOAD EBOOKThis marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.
Author: Wee Teck Gan
Publisher: Springer Science & Business Media
Published: 2007-12-22
Total Pages: 317
ISBN-13: 0817646396
DOWNLOAD EBOOKEisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. They have also been exploited extensively by number theorists for many arithmetic purposes. Bringing together contributions from areas which do not usually interact with each other, this volume introduces diverse users of Eisenstein series to a variety of important applications. With this juxtaposition of perspectives, the reader obtains deeper insights into the arithmetic of Eisenstein series. The central theme of the exposition focuses on the common structural properties of Eisenstein series occurring in many related applications.
Author: Greville G. Corbett
Publisher: Cambridge University Press
Published: 1993-06-24
Total Pages: 364
ISBN-13: 9780521402453
DOWNLOAD EBOOKA study of the idea of the 'head' or dominating element of a phrase.
Author: Jan H. Bruinier
Publisher: Springer
Published: 2004-10-11
Total Pages: 159
ISBN-13: 3540458727
DOWNLOAD EBOOKAround 1994 R. Borcherds discovered a new type of meromorphic modular form on the orthogonal group $O(2,n)$. These "Borcherds products" have infinite product expansions analogous to the Dedekind eta-function. They arise as multiplicative liftings of elliptic modular forms on $(SL)_2(R)$. The fact that the zeros and poles of Borcherds products are explicitly given in terms of Heegner divisors makes them interesting for geometric and arithmetic applications. In the present text the Borcherds' construction is extended to Maass wave forms and is used to study the Chern classes of Heegner divisors. A converse theorem for the lifting is proved.
Author: Nicholas Michael John Woodhouse
Publisher: Oxford University Press
Published: 2017
Total Pages: 201
ISBN-13: 0198784910
DOWNLOAD EBOOKThis book contains a series of chapters by leading researchers and practitioners on community engagement approaches in the field of counterterrorism and counterinsurgency. It presents existing and emerging community engagement models in various parts of the world which could serve as effective models for governments keen to work with community leaders to manage and reduce the terrorist threat. The book emphasizes the strength of communities as central to government approaches in countering violent extremism.