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Modular Forms and Special Cycles on Shimura Curves. (AM-161)
Stephen S. Kudla
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Description for Modular Forms and Special Cycles on Shimura Curves. (AM-161)
Paperback. A 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. Series: Annals of Mathematics Studies. Num Pages: 392 pages, 1 line illus. 3 tables. BIC Classification: PBH; PBKF. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 229 x 152 x 20. Weight in Grams: 542.
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 ... Read more
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 ... Read more
Product Details
Format
Paperback
Publication date
2006
Publisher
Princeton University Press United States
Number of pages
388
Condition
New
Series
Annals of Mathematics Studies
Number of Pages
392
Place of Publication
New Jersey, United States
ISBN
9780691125510
SKU
V9780691125510
Shipping Time
Usually ships in 7 to 11 working days
Ref
99-1
About Stephen S. Kudla
Stephen S. Kudla is at the University of Maryland. Michael Rapoport is at the Mathematisches Institut der Universitat, Bonn, Germany. Tonghai Yang is at the University of Wisconsin, Madison.
Reviews for Modular Forms and Special Cycles on Shimura Curves. (AM-161)
"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
Jens Funke, Mathematical Reviews