H. Gou

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20242026

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math.NT2026

On exponential sums with multiplicative coefficients

Haozhe Gou

Let $f : N \to z \in C : ∣ z ∣ \leq 1$ be multiplicative, and suppose that $α$ has a rational approximation $a / q$ with $∣ α - a / q ∣ \leq 1/ (q x)$ and $q\leq x/((\log x)^2(\log\lo…

math.NT2026

Logarithmic exponential sums with multiplicative coefficients

Haozhe Gou

Let $f$ be a $1$ -bounded multiplicative function, and suppose that $∣ α - a / q ∣ \leq 1/ (q x)$ , where $(a, q) = 1$ and $q \leq x$ . We prove that $$ \left|\sum_{n\leq x}\frac{f(n)}{n}e( nα)\ri…

math.NT2026

Large fluctuations of extended Rademacher random multiplicative functions

Haozhe Gou, Max Wenqiang Xu

Let $f$ be an extended Rademacher random multiplicative function (RMF). We show that, for every fixed deterministic function $V (x)$ tending to infinity, almost surely there are arb…

math.NT2026

Moments of the number of representations as sums of two prime squares

Haozhe Gou

We prove, for every fixed integer $k \geq 4$ , the correct order of magnitude for the $k$ th moments of the function that counts the number of representations of an integer as sums of…

math.NT2026

Extremal Problems for GCDs and LCMs in Higher Dimensions

Haozhe Gou

We study extremal problems for tuples of integers chosen from sets $A_{i} \subset [X_{i}, 2 X_{i}]$ for $1 \leq i \leq k$ , under large GCD and small LCM conditions. For the GCD problem, we ext…