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Markus Valås Hagen

Publications and source records attributed to Markus Valås Hagen.

6 recordsLinked to original sources
arXiv2026

Sharp unconditional moment bounds for products of L-functions

We investigate the mixed moments of products of irreducible $\mathrm{GL}(1)$ and $\mathrm{GL}(2)$ $L$-functions on the critical line, and establish sharp moment bounds for these quantities. In particular this establishes the order of these mixed moments in certain ranges. This determines unconditionally, for the first time, the order of magnitude of the first moment of cubic Dedekind zeta functions with negative discriminant. The proof of the lower bound introduces a new method for computing mixed moments, that is a mix of the classical method of Heath--Brown with the modern machinery of Harper, Heap, Radziwill, and Soundararajan.

math.NT↗
arXiv2025

On Goldbach numbers in short intervals

Assuming the Riemann Hypothesis, we prove that for all $x\geq 2$, there exists at least one even integer within the interval $(x, x+123\log^2x]$, that can be expressed as the sum of two primes. This result is an improvement over the recent work of Cully-Hugill and Dudek, who obtained the constant $9696$ instead of $123$.

math.NT↗
arXiv2024

Sharp conditional moment bounds for products of $L$-functions

Assuming the Generalized Riemann Hypothesis and the Generalized Ramanujan Conjecture, we determine the order of the $2(k_1,\dots,k_r)$th moment of a product of distinct irreducible $L$-functions on the critical line. As a consequence, we obtain conditional information about the independence of these $L$-functions in the large deviations regime. We also obtain sharp moment bounds for Hurwitz zeta functions with rational parameter, and a certain family of Dedekind zeta functions.

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arXiv2023

Conditional estimates for the logarithmic derivative of Dirichlet $L$-functions

Assuming the Generalized Riemann Hypothesis, we establish explicit bounds in the $q$-aspect for the logarithmic derivative $\left(L'/L\right)\left(σ,χ\right)$ of Dirichlet $L$-functions, where $χ$ is a primitive character modulo $q\geq 10^{30}$ and $1/2+1/\log{\log{q}}\leqσ\leq 1-1/\log\log q$. In addition, for $σ=1$ we improve upon the result by Ihara, Murty and Shimura (2009). Similar results for the logarithmic derivative of the Riemann zeta-function are given.

math.NT↗
arXiv2023

A dichotomy for extreme values of zeta and Dirichlet L-functions

We exhibit large values of the Dedekind zeta function of a cyclotomic field on the critical line. This implies a dichotomy whereby one either has improved lower bounds for the maximum of the Riemann zeta function, or large values of Dirichlet $L$-functions on the level of the Bondarenko--Seip bound.

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