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Number Theory 132 (2012), no

Yuk-Kam Lau, Lilu Zhao, On a variance of Hecke eigenvalues in arithmetic progressions , J · 2012 · DOI 10.1016/j.jnt.2011.12.011

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Variance of GL(2) Fourier coefficients in arithmetic progressions

math.NT · 2026-03-16 · unverdicted · novelty 5.0

The paper improves the known asymptotic for the variance of GL(2) Fourier coefficients of primitive cuspidal modular forms for SL(2,Z) in arithmetic progressions by combining bounds on the first moment of Rankin-Selberg L-functions in the height aspect with non-trivial estimates for shifted convolu

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  • Variance of GL(2) Fourier coefficients in arithmetic progressions math.NT · 2026-03-16 · unverdicted · none · ref 22

    The paper improves the known asymptotic for the variance of GL(2) Fourier coefficients of primitive cuspidal modular forms for SL(2,Z) in arithmetic progressions by combining bounds on the first moment of Rankin-Selberg L-functions in the height aspect with non-trivial estimates for shifted convolu