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Publications Influence

Updating the error term in the prime number theorem

- T. Trudgian
- Mathematics
- 13 January 2014

An improved estimate is given for $$|\theta (x) -x|$$|θ(x)-x|, where $$\theta (x) = \sum _{p\le x} \log p$$θ(x)=∑p≤xlogp. Four applications are given: the first to arithmetic progressions that have… Expand

37 8- PDF

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

- T. Trudgian
- Mathematics
- 29 August 2012

Abstract Text This paper concerns the function S ( T ) , where π S ( T ) is the argument of the Riemann zeta-function along the critical line. The main result is that | S ( T ) | ⩽ 0.112 log T +… Expand

56 6

Bounds on the number of Diophantine quintuples

- T. Trudgian
- Mathematics
- 19 January 2015

We consider Diophantine quintuples $\{a, b, c, d, e\}$. These are sets of distinct positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured… Expand

20 4- PDF

Linnik's approximation to Goldbach's conjecture, and other problems

- Dave Platt, T. Trudgian
- Mathematics
- 22 April 2014

We examine the problem of writing every sufficiently large even number as the sum of two primes and at most $K$ powers of 2. We outline an approach that only just falls short of improving the current… Expand

11 4- PDF

An improved explicit bound on $|ζ(1/2 + it)|$

- Dave Platt, T. Trudgian
- Mathematics
- 1 February 2015

Abstract This article proves the bound | ζ ( 1 2 + i t ) | ≤ 0.732 t 1 6 log t for t ≥ 2 , which improves on a result by Cheng and Graham. We also show that | ζ ( 1 2 + i t ) | ≤ 0.732 | 4.678 + i… Expand

20 3

On a conjecture of Shanks

- T. Trudgian
- Mathematics
- 1 December 2010

Abstract The conjecture in question concerns the function ϕ n related to the distribution of the zeroes of the Riemann zeta-function, γ n , over the Gram points g n . It is the purpose of this… Expand

14 3

There Are No Socialist Primes Less Than 109

- T. Trudgian
- Mathematics, Computer Science
- Integers
- 23 October 2013

There are no primes $p$ with $5<p<10^{9}$ for which $2!, 3!, \ldots, (p-1)!$ are all distinct modulo $p$; it is conjectured that there are no such primes.

5 2- PDF

Searching for Diophantine quintuples

- Mihai Cipu, T. Trudgian
- Mathematics
- 10 August 2015

We consider Diophantine quintuples $\{a, b, c, d, e\}$. These are sets of distinct positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured… Expand

13 2- PDF

The error term in the prime number theorem

- Dave Platt, T. Trudgian
- Computer Science, Mathematics
- Math. Comput.
- 10 September 2018

TLDR

7 2- PDF

On the success and failure of Gram's Law and the Rosser Rule

- T. Trudgian
- Mathematics
- 2011

This article contains a survey on results relating to Gram’s Law and the distribution of the zeroes of the Riemann zeta-function. It is shown that Gram’s Law and the Rosser Rule fail a positive… Expand

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