On the gaps in the Fourier expansion of cusp forms

DOI10.1007/s11139-007-9091-zzbMath1213.11100OpenAlexW1980041855MaRDI QIDQ935006

Alexandru Zaharescu, Emre Alkan

Publication date: 31 July 2008

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-007-9091-z

zbMATH Keywords

Fourier coefficientsComplex multiplicationCusp forms

Mathematics Subject Classification ID

Fourier coefficients of automorphic forms (11F30) Applications of sieve methods (11N36) Applications of automorphic functions and forms to multiplicative problems (11N75)

Related Items (7)

Gaps between nonzero Fourier coefficients of cusp forms ⋮ On the gaps between nonzero Fourier coefficients of eigenforms with CM ⋮ On the gaps between non-zero Fourier coefficients of cusp forms of higher weight ⋮ On sums over the Möbius function and discrepancy of fractions ⋮ Statistics and characterization of matrices by determinant and trace ⋮ On Dirichlet \(L\)-functions with periodic coefficients and Eisenstein series ⋮ A note on small gaps between nonzero Fourier coefficients of cusp forms

Cites Work

• Quelques applications du théorème de densité de Chebotarev
• Ramanujan's unpublished manuscript on the partition and tau functions with proofs and commentary
• On automorphic forms on \(mathrm{GL}_2\) and Hecke operators
• The vanishing of Ramanujan's function \(\tau(n)\)
• Nonvanishing of Fourier coefficients of newforms in progressions
• Nonvanishing of Fourier coefficients of modular forms
• On the Sizes of Gaps in the Fourier Expansion of Modular Forms
• The Chebotarev density theorem in short intervals and some questions of Serre
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