Bounds for short character sums for GL(2) × GL(3) twists

2021/11/18 by Aritra Ghosh, Ghosh, Aritra
Mathematics · Social Sciences · #Analytic Number Theory Research #Advanced Algebra and Geometry #Historical Geopolitical and Social Dynamics

paper · pdf · doi:10.48550/arxiv.2111.09524

Abstract

Let π be a SL(3,ℤ) Hecke Maass-cusp form, f be a SL(2,ℤ) holomorphic cusp form or Maass-cusp form with normalized Fourier coefficients λ_π(r,n) and λ_f(n) respectively and χ be any non-trivial character mod p where p is a prime. Then we have S_π,f,χ(N)≪_{π, f, ε} N^3/4p^11/16 +η/4(Np)^ε.

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