Tianyu Zhao

collaborators

6 papers

math.NT2026

Upper bounds on gaps between zeros of $L$ -functions

Tianyu Zhao

We prove two unconditional upper bounds on the gaps between ordinates of consecutive non-trivial zeros of a general $L$ -function $L (s)$ . This extends previous work of Hall and Haym…

math.NT2026

Unconditional estimates on the argument of Dirichlet $L$ -functions with applications to low-lying zeros

Ghaith Hiary, Tianyu Zhao

We make explicit a result of Selberg on the argument of Dirichlet $L$ -functions averaged over non-principal characters modulo a prime $q$ . As a corollary, we show for all sufficien…

math.NT2026

Conditional estimates on the argument of Dirichlet $L$ -functions with applications to low-lying zeros

Tianyu Zhao

Under the generalized Riemann hypothesis, we use Beurling-Selberg extremal functions to bound the mean and mean square of the argument of Dirichlet $L$ -functions to a large prime m…

math.NT2026

Density results for $r$ -gaps between zeros of the Riemann zeta-function

Tianyu Zhao

Let $0 < I^_{1}^{3} \leq I^_{2}^{3} \leq \dots$ denote the positive ordinates of the non-trivial zeros of the Riemann zeta-function. A result first announced by Selberg states that there exist ab…

math.NT2025

On Turing's method for a general set of $L$ -functions and the Selberg class

Neea PalojÃ¤rvi, Neea Palojärvi, Tianyu Zhao

We derive explicit bounds for two general classes of $L$ -functions, improving and generalizing earlier known estimates. These bounds can be used, for example, to apply Turing's met…

math.NT2025

The positivity technique and low-lying zeros of Dirichlet $L$ -functions

Tianyu Zhao

Assuming the generalized Riemann hypothesis, we sharpen the error terms in a number of estimates related to the distribution of low-lying zeros of Dirichlet $L$ -functions. The refi…

Upper bounds on gaps between zeros of L-functions

Unconditional estimates on the argument of Dirichlet L-functions with applications to low-lying zeros

Conditional estimates on the argument of Dirichlet L-functions with applications to low-lying zeros

Density results for r-gaps between zeros of the Riemann zeta-function

On Turing's method for a general set of L-functions and the Selberg class

The positivity technique and low-lying zeros of Dirichlet L-functions

Upper bounds on gaps between zeros of $L$ -functions

Unconditional estimates on the argument of Dirichlet $L$ -functions with applications to low-lying zeros

Conditional estimates on the argument of Dirichlet $L$ -functions with applications to low-lying zeros

Density results for $r$ -gaps between zeros of the Riemann zeta-function

On Turing's method for a general set of $L$ -functions and the Selberg class

The positivity technique and low-lying zeros of Dirichlet $L$ -functions