Songlin Han

collaborators

4 papers

math.NT2026

On variants of Pólya's conjecture

Songlin Han

In this paper, we study a Riesz-type weighted sum of the Liouville function, $f (x) := - \sum_{n \leq x} \frac{λ ( n ) l o g n}{n} lo g \frac{x}{n}$ for sufficiently large $x$ . Motivated b…

math.NT2026

Positive density for Sun's $2^{k} + m$ conjecture

Songlin Han, Jinbo Yu

In 2013, Zhi-Wei Sun proposed a Romanov-type conjecture stating that every integer $n > 1$ can be written as $n = k + m$ with $k, m \geq 1$ such that $2^{k} + m$ is a prime. In this p…

math.NT2026

Almost-primes in Sun's $x^{2} + n y^{2}$ conjecture

Songlin Han, Jinbo Yu

In 2015 Zhi-Wei Sun proposed the conjecture that any integer $n > 1$ admits a partition $n = x + y$ with integers $x, y > 0$ such that $x + n y$ and $x^{2} + n y^{2}$ are simultaneously p…

math.NT2025

The Error in a Smooth Weighted Prime Number Formula and Zero-free Regions for the Riemann Zeta Function

Songlin Han

We study the error bound for a smooth weighted prime number theorem, and its implication to the zero-free region for the Riemann zeta function using the method of Pintz. We also gi…

On variants of Pólya's conjecture

Positive density for Sun's 2k+m conjecture

Almost-primes in Sun's x2+ny2 conjecture

The Error in a Smooth Weighted Prime Number Formula and Zero-free Regions for the Riemann Zeta Function

Positive density for Sun's $2^{k} + m$ conjecture

Almost-primes in Sun's $x^{2} + n y^{2}$ conjecture