Benford’s Law for coefficients of newforms
Abstract
Let f(z)=∑∞n=1λf(n)e2πinz∈Snewk(Γ0(N))f(z)=∑∞n=1λf(n)e2πinz∈Snewk(Γ0(N)) be a newform of even weight k≥2k≥2 on Γ0(N)Γ0(N) without complex multiplication. Let ℙ denote the set of all primes. We prove that the sequence {λf(p)}p∈ℙ does not satisfy Benford’s Law in any integer base b≥2. However, given a base b≥2 and a string of digits S in base b, the set
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