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:2402.06426 , year =
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
fields
math.NT 3years
2026 3verdicts
UNVERDICTED 3representative citing papers
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}).
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}.
citing papers explorer
-
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.
-
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}).
-
Character sums over smooth numbers
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}.