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On the Fourier coefficients of modular forms of half-integral weight
Published/Copyright:
October 5, 2009
Abstract
We prove a formula relating the Fourier coefficients of a modular form of half-integral weight to the special values of L-functions. The form in question is an explicit theta lift from the multiplicative group of an indefinite quaternion algebra over ℚ. This formula has applications to proving the nonvanishing of this lift and to an explicit version of the Rallis inner product formula.
Received: 2007-08-01
Accepted: 2008-05-11
Published Online: 2009-10-05
Published in Print: 2010-January
© de Gruyter 2010
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Articles in the same Issue
- Ideals in non-associative universal enveloping algebras of Lie triple systems
- Curvature of almost quaternion-Hermitian manifolds
- Lp-moduli of continuity of sections of functions
- No invariant line fields on Cantor Julia sets
- Chain conditions for Leavitt path algebras
- On differentiability of quermassintegrals
- The number of configurations in lattice point counting I
- On the Fourier coefficients of modular forms of half-integral weight
- Cross-ratio in higher rank symmetric spaces
- Local characterizations of infinite groups whose ascendant subgroups are permutable
