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 2013 · math.NTShow all

6 papers · 2 filters

math.NT2013

A log-free zero-density estimate and small gaps in coefficients of $L$ -functions

Amir Akbary, Timothy S. Trudgian

Let $L (s, π \times π^{'})$ be the Rankin--Selberg $L$ -function attached to automorphic representations $π$ and $π^{'}$ . Let $π ~$ and $π ~^{'}$ denote the contragred…

math.NT2013

The sum of the unitary divisor function

Tim Trudgian

This article establishes a new upper bound on the function $σ^{*} (n)$ , the sum of all coprime divisors of $n$ . The article concludes with two questions concerning this function.

math.NT2013

A short extension of two of Spira's results

Tim Trudgian

Two inequalities concerning the symmetry of the zeta-function and the Ramanujan $τ$ -function are improved through the use of some elementary considerations.

math.NT2013

An incomplete variant of Wilson's congruence

Joel Beeren, David Harvey, Tim Trudgian

This article examines the nontrivial solutions of the congruence \[ (p-1)\cdots(p-r) \equiv -1 \pmod p. \] We discuss heuristics for the proportion of primes $p$ that have exactly…

math.NT2013★ 2 cited

There are no socialist primes less than 10^9

Tim Trudgian

There are no primes $p$ with $5 < p < 1 0^{9}$ for which $2!, 3!, \dots, (p - 1)!$ are all distinct modulo $p$ ; it is conjectured that there are no such primes.

math.NT2013★ 1 cited

A poor man's improvement on Zhang's result: there are infinitely many prime gaps less than 60 million

T. S. Trudgian

Taking the easy option I prove that one can lower Zhang's bound on prime gaps from 70 million to 60 million. A poor man's improvement indeed!

A log-free zero-density estimate and small gaps in coefficients of L-functions

The sum of the unitary divisor function

A short extension of two of Spira's results

An incomplete variant of Wilson's congruence

There are no socialist primes less than 10^9

A poor man's improvement on Zhang's result: there are infinitely many prime gaps less than 60 million

A log-free zero-density estimate and small gaps in coefficients of $L$ -functions