The order of magnitude of E|sum_{n≤x} h(n)λ(n)|^{2q} is determined for 0≤q≤1 where h is Steinhaus or Rademacher random multiplicative and λ comes from a fixed modular form.
Selberg,Bemerkungen ¨ uber eine Dirichletsche Reihe, die mit der Theorie der Modulformen nahe verbunden ist, Arch
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Low moments of random multiplicative functions twisted by Fourier coefficients of modular forms
The order of magnitude of E|sum_{n≤x} h(n)λ(n)|^{2q} is determined for 0≤q≤1 where h is Steinhaus or Rademacher random multiplicative and λ comes from a fixed modular form.