Tim Trudgian

collaborators

4 papers

math.NT2025

Applying hypersurface bounds to a conjecture by Carlet

ZoÃ« Gemmell, Tim Trudgian

A function from $F_{2^{n}}$ to $F_{2^{n}}$ is $k$ th order sum-free if the sum of its values over each $k$ -dimensional $F_{2}$ -affine subspace is nonzero. It is…

math.NT2025

The determination of norm-Euclidean cyclic cubic fields

Gustav KjÃ¦rbye Bagger, Gustav Kjærbye Bagger, Andrew R. Booker +5

It is known on the Generalised Riemann Hypothesis that there are precisely $13$ cyclic cubic fields that are norm-Euclidean. Unconditionally, there is a gap between analytic estima…

math.NT2025

On the error term of the fourth moment of the Riemann zeta-function

Neea PalojÃ¤rvi, Tim Trudgian

We examine the size of $E_{2} (T)$ , the error term in the asymptotic formula for $\int_{0}^{T} ∣ I^¶ (1/2 + i t) ∣^{4} d t$ where $I^¶ (s)$ is the Riemann zeta-function. We make improveme…

math.NT2025

New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach

Terence Tao, Tim Trudgian, Andrew Yang

We obtain several new bounds on exponents of interest in analytic number theory, including four new exponent pairs, new zero density estimates for the Riemann zeta-function, and ne…