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

Showing 2012 · math.NTShow all

4 papers · 2 filters

math.NT2012★ 17 cited

A new upper bound for $∣ ζ (1 + i t) ∣$

Timothy Trudgian

It is known that $∣ ζ (1 + i t) ∣ ≪ (lo g t)^{2/3}$ . This paper provides a new explicit estimate, viz.\ $∣ ζ (1 + i t) ∣ \leq 3/4 lo g t$ , for $t \geq 3$ . This gives the best upper bound on $…

math.NT2012★ 2 cited

An improved upper bound for the argument of the Riemann zeta-function on the critical line II

T. S. Trudgian

This paper improves the bound on $∣ S (T) ∣$ . The main result is to show that $∣ S (T) ∣ \leq 0.111 lo g T + 0.275 lo g lo g T + 2.450$ , which is valid for all $T \geq e$ .

math.NT2012★ 1 cited

Linear relations of zeroes of the zeta-function

Darcy Best, Tim Trudgian

This article considers linear relations between the non-trivial zeroes of the Riemann zeta-function. The main application is an alternative disproof to Mertens' conjecture. We show…

math.NT2012★ 1 cited

An improved upper bound for the error in the zero-counting formulae for Dirichlet $L$ -functions and Dedekind zeta-functions

T. S. Trudgian

This paper contains new explicit upper bounds for the number of zeroes of Dirichlet L-functions and Dedekind zeta-functions in rectangles.

A new upper bound for ∣ζ(1+it)∣

An improved upper bound for the argument of the Riemann zeta-function on the critical line II

Linear relations of zeroes of the zeta-function

An improved upper bound for the error in the zero-counting formulae for Dirichlet L-functions and Dedekind zeta-functions

A new upper bound for $∣ ζ (1 + i t) ∣$

An improved upper bound for the error in the zero-counting formulae for Dirichlet $L$ -functions and Dedekind zeta-functions