T. Trudgian

activity

20082023

most citedAccurate estimation of sums over zeros of the Riemann zeta-function

20 citations · 104 across the 42 of their papers we have counts for

collaborators

62 papers

math.NT2023★ 2 cited

Toward optimal exponent pairs

Timothy S. Trudgian, Andrew Yang

We quantify the set of known exponent pairs $(k, ℓ)$ and develop a framework to compute the optimal exponent pair for an arbitrary objective function. Applying this methodology,…

math.NT2023

An explicit upper bound for $L (1, χ)$ when $χ$ is quadratic

D. R. Johnston, O. Ramare, T. S. Trudgian

We consider Dirichlet $L$ -functions $L (s, χ)$ where $χ$ is a non-principal quadratic character to the modulus $q$ . We make explicit a result due to Pintz and Stephens by showing th…

math.NT2022

Explicit zero-free regions for the Riemann zeta-function

Michael J. Mossinghoff, Timothy S. Trudgian, Andrew Yang

We prove that the Riemann zeta-function $ζ (σ + i t)$ has no zeros in the region $σ \geq 1 - 1/ (55.241 (lo g ∣ t ∣)^{2/3} (lo g lo g ∣ t ∣)^{1/3})$ for $∣ t ∣ \geq 3$ . In addition, we improve th…

math.NT2022★ 1 cited

On the Montgomery-Odlyzko method regarding gaps between zeros of the zeta-function

Daniel A. Goldston, Timothy S. Trudgian, Caroline L. Turnage-Butterbaugh

Assuming the Riemann Hypothesis, it is known that there are infinitely many consecutive pairs of zeros of the Riemann zeta-function within 0.515396 times the average spacing. This…

math.NT2021

Fake Mu's

Greg Martin, Michael J. Mossinghoff, Timothy S. Trudgian

Let $f (n)$ denote a multiplicative function with range ${- 1, 0, 1}$ , and let $F (x) = \sum_{n \leq x} f (n)$ . Then $F (x) / x = a x + b + E (x)$ , where $a$ and $b$ are consta…

math.NT2021

Primitive elements with prescribed traces

Andrew R. Booker, Stephen D. Cohen, Nicol Leong +1

Given a prime power $q$ and a positive integer $n$ , let $F_{q^{n}}$ denote the finite field with $q^{n}$ elements. Also let $a, b$ be arbitrary members of the ground field $\…