Additive bases with coefficients of newforms

2017/03/24 by Garcia, Victor Cuauhtemoc, Nicolae, Florin
#11F30 #11P05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1703.08473

Abstract

Let f(z)=∑_n=1^∞a(n) e^{2πi nz} be a normalized Hecke eigenform in S_2k^new(Γ₀(N)) with integer Fourier coefficients. We prove that there exists a constant C(f)>0 such that any integer is a sum of at most C(f) coefficients a(n) . It holds C(f)≪_ε,kN^{(6k-3)/(16)+ε}.

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