H. Gou

activity

20242026

collaborators

7 papers

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…

math.NT2025

Explicit bounds for the graphicality of the prime gap sequence

Keshav Aggarwal, Robin Frot, Haozhe Gou +1

We establish explicit unconditional results on the graphic properties of the prime gap sequence. Let $p_{n}$ denote the $n$ -th prime number (with $p_{0} = 1$ ) and $\mathrm{PD}_n = (p_\el…

math.NT2024

On the Second Moment of Twisted Higher Degree $L$ -functions

Haozhe Gou, Liangxun Li

Assuming the Ramanujan conjecture, the zero density estimate and some subconvexity type bound, we describe a general method to obtain the log-saving upper bound for the second mome…

On exponential sums with multiplicative coefficients

Logarithmic exponential sums with multiplicative coefficients

Large fluctuations of extended Rademacher random multiplicative functions

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

Extremal Problems for GCDs and LCMs in Higher Dimensions

Explicit bounds for the graphicality of the prime gap sequence

On the Second Moment of Twisted Higher Degree L-functions

On the Second Moment of Twisted Higher Degree $L$ -functions