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HECKE-SIEGEL TYPE THRESHOLD FOR SQUARE-FREE FOURIER COEFFICIENTS : AN IMPROVEMENT (Analytic and Arithmetic Theory of Automorphic Forms)

open access: yesHECKE-SIEGEL TYPE THRESHOLD FOR SQUARE-FREE FOURIER COEFFICIENTS : AN IMPROVEMENT (Analytic and Arithmetic Theory of Automorphic Forms)
We prove that if f is a non zero cusp form of weight k on Gamma_{0}(N) with character chi such that N/(conductor chi) is square-free, and epsilon>0 is given, then there exists a square-free nleq k^{3+epsilon}N^{7/2+epsilon} such that a(f, n)neq 0. This significantly improves the already known existential and quantitative result from previous works.
openaire   +1 more source

Automorphic L-functions of half-integral weight. [PDF]

open access: yesProc Natl Acad Sci U S A, 1978
Gelbart SS, Piatetski-Shapiro II.
europepmc   +1 more source

Canonicalizing Zeta Generators: Genus Zero and Genus One. [PDF]

open access: yesCommun Math Phys
Dorigoni D   +7 more
europepmc   +1 more source

Geometry and physics. [PDF]

open access: yesPhilos Trans A Math Phys Eng Sci, 2010
Atiyah M, Dijkgraaf R, Hitchin N.
europepmc   +1 more source

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