Under GRH, the order of magnitude of E|sum_{n≤x} h(n) λ(n)|^{2q} is determined up to e^{O(q^2)} for 1 ≤ q ≤ c log x / log log x.
Low moments of random multiplicative functions twisted by Fourier coefficients of modular forms
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Let $\lambda(n)$ denote the Fourier coefficients of a fixed modular form and $h(n)$ a Steinhaus or Rademacher random multiplicative function. In this paper, we determine the order of magnitude of \[ \E|\sum_{n \leq x} h(n)\lambda(n)|^{2q} \] for real $x$, $q$ with $0 \leq q \leq 1$.
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2026 1verdicts
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High moments of random multiplicative functions twisted by Fourier coefficients of modular forms
Under GRH, the order of magnitude of E|sum_{n≤x} h(n) λ(n)|^{2q} is determined up to e^{O(q^2)} for 1 ≤ q ≤ c log x / log log x.