For α in (1,2) the expected 2q-moment of the normalized sum of d_α(n) f(n) is bounded by (log x)^{2q(α-1)} over a power of log log x, uniformly for q up to 1/α.
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Under RH, the measure of t in [T,2T] with |zeta(1/2+it)| > (log T)^k is <= C_k (log T)^{-k^2}/sqrt(log log T) with C_k=exp(e^{ck}), implying 2k-moment bounds C_k (log T)^{k^2}.
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Partial sums of random multiplicative functions with supercritical divisor twists
For α in (1,2) the expected 2q-moment of the normalized sum of d_α(n) f(n) is bounded by (log x)^{2q(α-1)} over a power of log log x, uniformly for q up to 1/α.
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Conditional Upper Bounds for Large Deviations and Moments of the Riemann Zeta Function
Under RH, the measure of t in [T,2T] with |zeta(1/2+it)| > (log T)^k is <= C_k (log T)^{-k^2}/sqrt(log log T) with C_k=exp(e^{ck}), implying 2k-moment bounds C_k (log T)^{k^2}.
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