Genheng Zhao

collaborators

4 papers

math.NT2026

The exceptional set of Goldbach problem and Linnik's constant

Genheng Zhao

Let $E (X)$ denote the number of even integers below $X$ which are not a sum of two primes. We prove the bound $E (X) = O (X^{\frac{7}{10}})$ , where the implicit constant is ineffective…

math.NT2025

Logarithmic derivatives of L-functions and small prime quadratic nonresidues

Genheng Zhao

Let $I ¨ $ be a real non-principal character modulo a prime $q$ and $L (s, I ¨ )$ be the corresponding $L$ -function. We prove that for any real number $s \geq 1$ there holds $$ -\frac{L'(…

math.NT2025

On sums of finite subsets of the primes

Genheng Zhao

Let $A \subset [1, x]$ be a non-empty set of primes with $∣ A ∣ = I^\pm x (lo g x)^{- 1}$ . We prove that there exist absolute constants $c_{1}, c_{2} > 0$ such that, as $x$ gets sufficiently large,…

math.NT2025

A density theorem for prime squares

Genheng Zhao

Let $s \geq 8$ be an integer and $P$ be a set of primes with relative lower density greater than $1 - min {s, 16} /32$ . We prove that every sufficiently large integer $n\equiv…