PERIODS OF EISENSTEIN AND POINCARÉ SERIES

Leon Ehrenpreis

doi:10.1093/acprof:oso/9780198509783.003.0010

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PERIODS OF EISENSTEIN AND POINCARÉ SERIES

Leon Ehrenpreis

Year: 2003 Oxford University Press eBooks Pages: 580-670 Publisher: Oxford University Press

DOI: 10.1093/acprof:oso/9780198509783.003.0010

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Abstract

This chapter shows how the book's main theory applies to computing the periods of Eisenstein and Poincaré series. Our Poincaré series are eigenfunctions of the Laplacian, and they arise naturally in the theory. In particular, the periods of the Poincaré series are Kloosterman sums.

Keywords:

Poincaré series Eisenstein series Series (stratigraphy) Mathematics Eigenfunction Poincaré conjecture Kloosterman sum Pure mathematics Laplace operator Algebra over a field Mathematical analysis Physics Eigenvalues and eigenvectors Quantum mechanics Modular form

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Physical Sciences → Mathematics → Geometry and Topology

PERIODS OF EISENSTEIN AND POINCARÉ SERIES

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