Proves that (1/φ(q)) ∑_χ |∑_{n≤x, P(n)≤y} χ(n)| = o(√Ψ(x,y)) for (log x)^6 ≤ y ≤ x^{1/(32 log log x)} and q ≥ x^{1+ε}.
Harper.The typical size of character and zeta sums iso( √x), https://arxiv.org/abs/2301.04390
5 Pith papers cite this work. Polarity classification is still indexing.
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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.
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.
Establishes sharp lower bounds matching prior upper bounds for moments of short character sums, zeta sums, and twisted sums with multiplicative weights, for x up to r^0.499.
Obtains unrestricted high-moment estimates and exponential tail bounds for sums of Rademacher multiplicative functions via martingales.
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A few notes on the asymptotic behavior of Rademacher random multiplicative functions
Obtains unrestricted high-moment estimates and exponential tail bounds for sums of Rademacher multiplicative functions via martingales.