TY - JOUR

T1 - Central critical values of modular L-functions and coefficients of half-integral weight modular forms modulo ℓ

AU - Ahlgren, Scott

AU - Boylan, Matthew

PY - 2007/4

Y1 - 2007/4

N2 - If F(z) is a newform of weight 2λ and D is a fundamental discriminant, then let L(F ⊗ΧD, s) be the usual twisted L-series. We study the algebraic parts of the central critical values of these twisted L-series modulo primes ℓ. We show that if there are two D (subject to some local conditions) for which the algebraic part of L(F ⊗ ΧD, λ) in not 0 (mod ℓ), then there are infinitely many such D. These results depend on precise nonvanishing results for the Fourier coefficients of half-integral weight modular forms modulo ℓ, which are of independent interest.

AB - If F(z) is a newform of weight 2λ and D is a fundamental discriminant, then let L(F ⊗ΧD, s) be the usual twisted L-series. We study the algebraic parts of the central critical values of these twisted L-series modulo primes ℓ. We show that if there are two D (subject to some local conditions) for which the algebraic part of L(F ⊗ ΧD, λ) in not 0 (mod ℓ), then there are infinitely many such D. These results depend on precise nonvanishing results for the Fourier coefficients of half-integral weight modular forms modulo ℓ, which are of independent interest.

UR - http://www.scopus.com/inward/record.url?scp=34248581177&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34248581177&partnerID=8YFLogxK

U2 - 10.1353/ajm.2007.0006

DO - 10.1353/ajm.2007.0006

M3 - Article

AN - SCOPUS:34248581177

SN - 0002-9327

VL - 129

SP - 429

EP - 454

JO - American Journal of Mathematics

JF - American Journal of Mathematics

IS - 2

ER -