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Overview"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." Full Product DetailsAuthor: Stephen S. Kudla , Michael Rapoport , Tonghai YangPublisher: Princeton University Press Imprint: Princeton University Press Volume: 175 Dimensions: Width: 15.20cm , Height: 2.00cm , Length: 23.50cm Weight: 0.539kg ISBN: 9780691125510ISBN 10: 0691125511 Pages: 392 Publication Date: 24 April 2006 Audience: Professional and scholarly , College/higher education , Professional & Vocational , Tertiary & Higher Education Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Language: English Table of ContentsReviewsThis 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 """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" 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 Author InformationStephen S. Kudla is at the University of Maryland. Michael Rapoport is at the Mathematisches Institut der Universitt, Bonn, Germany. Tonghai Yang is at the University of Wisconsin, Madison. Tab Content 6Author Website:Countries AvailableAll regions |
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