Unconditional asymptotic formula for moments of S(t,f) for Hecke cusp forms of prime level q, implying a weighted central limit theorem for S(t,f) normalized by sqrt(log log q).
Shimura, Introduction to the arithmetic theory of automorphic funct ions
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On a level analog of Selberg's result on $S(t)$
Unconditional asymptotic formula for moments of S(t,f) for Hecke cusp forms of prime level q, implying a weighted central limit theorem for S(t,f) normalized by sqrt(log log q).