Automorphic Forms, Shimura Varieties, and L-functions PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Automorphic Forms, Shimura Varieties, and L-functions PDF full book. Access full book title Automorphic Forms, Shimura Varieties, and L-functions by Laurent Clozel. Download full books in PDF and EPUB format.
Author: Laurent Clozel
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 464
Get Book Here
Book Description
Author: Laurent Clozel
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 464
Get Book Here
Book Description
Author: Laurent Clozel
Publisher:
ISBN: 9780121766528
Category : Automorphic forms
Languages : en
Pages :
Get Book Here
Book Description
Author: Laurent Clozel
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
Book Description
Author: Armand Borel
Publisher: American Mathematical Soc.
ISBN: 0821814370
Category : Mathematics
Languages : en
Pages : 394
Get Book Here
Book Description
Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions
Author: Haruzo Hida
Publisher: Springer Science & Business Media
ISBN: 9780387207117
Category : Mathematics
Languages : en
Pages : 414
Get Book Here
Book Description
This book covers the following three topics in a manner accessible to graduate students who have an understanding of algebraic number theory and scheme theoretic algebraic geometry: 1. An elementary construction of Shimura varieties as moduli of abelian schemes. 2. p-adic deformation theory of automorphic forms on Shimura varieties. 3. A simple proof of irreducibility of the generalized Igusa tower over the Shimura variety. The book starts with a detailed study of elliptic and Hilbert modular forms and reaches to the forefront of research of Shimura varieties associated with general classical groups. The method of constructing p-adic analytic families and the proof of irreducibility was recently discovered by the author. The area covered in this book is now a focal point of research worldwide with many far-reaching applications that have led to solutions of longstanding problems and conjectures. Specifically, the use of p-adic elliptic and Hilbert modular forms have proven essential in recent breakthroughs in number theory (for example, the proof of Fermat's Last Theorem and the Shimura-Taniyama conjecture by A. Wiles and others). Haruzo Hida is Professor of Mathematics at University of California, Los Angeles. His previous books include Modular Forms and Galois Cohomology (Cambridge University Press 2000) and Geometric Modular Forms and Elliptic Curves (World Scientific Publishing Company 2000).
Author: Yuval Z. Flicker
Publisher: World Scientific
ISBN: 9812703322
Category : Mathematics
Languages : en
Pages : 340
Get Book Here
Book Description
The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called OC liftings.OCO This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the natural embedding of Sp(2, ?) in SL(4, ?). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic PGSp(2) by means of a definition of packets and quasi-packets, using character relations and trace formulae identities. It also shows multiplicity one and rigidity theorems for the discrete spectrum. Applications include the study of the decomposition of the cohomology of an associated Shimura variety, thereby linking Galois representations to geometric automorphic representations. To put these results in a general context, the book concludes with a technical introduction to LanglandsOCO program in the area of automorphic representations. It includes a proof of known cases of ArtinOCOs conjecture."
Author: James S. Milne
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
Book Description
Author: Ze-Li Dou
Publisher: Springer Science & Business Media
ISBN: 3642287085
Category : Mathematics
Languages : en
Pages : 131
Get Book Here
Book Description
"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.
Author: Haruzo Hida
Publisher: Springer Science & Business Media
ISBN: 1468493906
Category : Mathematics
Languages : en
Pages : 397
Get Book Here
Book Description
In the early years of the 1980s, while I was visiting the Institute for Ad vanced Study (lAS) at Princeton as a postdoctoral member, I got a fascinating view, studying congruence modulo a prime among elliptic modular forms, that an automorphic L-function of a given algebraic group G should have a canon ical p-adic counterpart of several variables. I immediately decided to find out the reason behind this phenomenon and to develop the theory of ordinary p-adic automorphic forms, allocating 10 to 15 years from that point, putting off the intended arithmetic study of Shimura varieties via L-functions and Eisenstein series (for which I visited lAS). Although it took more than 15 years, we now know (at least conjecturally) the exact number of variables for a given G, and it has been shown that this is a universal phenomenon valid for holomorphic automorphic forms on Shimura varieties and also for more general (nonholomorphic) cohomological automorphic forms on automorphic manifolds (in a markedly different way). When I was asked to give a series of lectures in the Automorphic Semester in the year 2000 at the Emile Borel Center (Centre Emile Borel) at the Poincare Institute in Paris, I chose to give an exposition of the theory of p-adic (ordinary) families of such automorphic forms p-adic analytically de pending on their weights, and this book is the outgrowth of the lectures given there.
Author: Laurent Clozel
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 416
Get Book Here
Book Description
