Free shipping on orders over $89 - Limited time only - T&Cs apply
Track My Order
Help Centre
Likes
My Wish ListsLogin / Join
Booktopia
Australia's local bookstore
Get Free Shipping on orders over $89
Modular Forms and Special Cycles on Shimura Curves. (AM-161) : Annals of Mathematics Studies - Stephen S. Kudla

Modular Forms and Special Cycles on Shimura Curves. (AM-161)

By: Stephen S. Kudla, Michael Rapoport, Tonghai Yang

Paperback | 3 July 2006

At a Glance

Paperback

RRP $180.00

$140.99

22%OFF

or 4 interest-free payments of $35.25 with

 or 

Ships in 3 to 5 business days

Modular Forms and Special Cycles on Shimura Curves is a thorough study of the generating functions constructed from special cycles, both divisors and zero-cycles, on the arithmetic surface "M" attached to a Shimura curve "M" over the field of rational numbers. These generating functions are shown to be the q-expansions of modular forms and Siegel modular forms of genus two respectively, valued in the Gillet-Soule arithmetic Chow groups of "M". The two types of generating functions are related via an arithmetic inner product formula. In addition, an analogue of the classical Siegel-Weil formula identifies the generating function for zero-cycles as the central derivative of a Siegel Eisenstein series. As an application, an arithmetic analogue of the Shimura-Waldspurger correspondence is constructed, carrying holomorphic cusp forms of weight 3/2 to classes in the Mordell-Weil group of "M". In certain cases, the nonvanishing of this correspondence is related to the central derivative of the standard L-function for a modular form of weight 2. These results depend on a novel mixture of modular forms and arithmetic geometry and should provide a paradigm for further investigations. The proofs involve a wide range of techniques, including arithmetic intersection theory, the arithmetic adjunction formula, representation densities of quadratic forms, deformation theory of p-divisible groups, p-adic uniformization, the Weil representation, the local and global theta correspondence, and the doubling integral representation of L-functions.

Industry Reviews
"This book represents a major milestone for research at the intersection of arithmetic geometry and automorphic forms. The results will shape the research in this area for some time to come."--Jens Funke, Mathematical Reviews

You Can Find This Book In

Non-FictionMathematicsGeometryAlgebraic GeometryNumber TheoryCalculus & Mathematical AnalysisFunctional Analysis & Transforms

More in Functional Analysis & Transforms

Abstract Cauchy Problems : Three Approaches - Irina V. Melnikova

Abstract Cauchy Problems

Three Approaches

Hardcover

RRP $315.00

$271.99

14%
OFF
A Visual Approach to Introductory Functional Analysis - Paul Dayao

A Visual Approach to Introductory Functional Analysis

Hardcover

RRP $200.00

$176.75

12%
OFF
Schaum's Outline of Complex Variables : Schaum's Outline Series - Murray R. Spiegel

Schaum's Outline of Complex Variables

Schaum's Outline Series

Paperback

RRP $63.95

$45.75

28%
OFF

This product is categorised by