Sums of Steinhaus random multiplicative functions over short intervals [x, x+y] (y→∞, y=o(x)) have Gaussian limiting distributions after a normalization that is not √y when y is close to x.
arXiv preprint arXiv:2503.06256 , year =
3 Pith papers cite this work. Polarity classification is still indexing.
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Proves that sum of Steinhaus random multiplicative function over A converges to CN(0,1) only if |A|=o(N), with sharpness for most sets of density ρ where (1-ρ)^{-1}=o((log log N)^{1/2}).
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.
citing papers explorer
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Distribution of random multiplicative functions in short intervals, with proper normalization
Sums of Steinhaus random multiplicative functions over short intervals [x, x+y] (y→∞, y=o(x)) have Gaussian limiting distributions after a normalization that is not √y when y is close to x.
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Escaping Chaos in Random Multiplicative Functions
Proves that sum of Steinhaus random multiplicative function over A converges to CN(0,1) only if |A|=o(N), with sharpness for most sets of density ρ where (1-ρ)^{-1}=o((log log N)^{1/2}).
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Lower bounds for low moments of character sums, I: Short sums with general multiplicative weights
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.