arXiv subjects

Mikko Jaskari

Publications and source records attributed to Mikko Jaskari.

3 recordsLinked to original sources

arXiv2026

Explicit bounds for the prime number theorem

We study the problem of finding tight explicit bounds on sums over zeros of $L$-functions near the $1$-line with a variety of zero-free regions and zero-density estimates. As an application to demonstrate the techniques, we apply them to the case of the Riemann zeta function and the prime number theorem to obtain new best estimates on the error terms in the prime number theorem. We show that for $x\geq21$ we have $|ψ(x)-x| < 0.239 x \exp\left(-0.1982767\left(1+\frac{\log\log\log(x)}{15\log\log(x)}\right) \frac{\log(x)^{3/5}}{\log\log(x)^{1/5}}\right).$

math.NT↗

arXiv2026

The Chowla conjecture and Landau-Siegel zeroes

Let $k\geq 2$ be an integer and let $λ$ be the Liouville function. Given $k$ non-negative distinct integers $h_1,\ldots,h_k$, the Chowla conjecture claims that $\sum_{n\leq x}λ(n+h_1)\cdots λ(n+h_k)=o(x)$ as $x\to\infty$. An unconditional answer to this conjecture is yet to be found, and in this paper, we take a conditional approach towards it. More precisely, we establish a non-trivial bound for the sums $\sum_{n\leq x}λ(n+h_1)\cdots λ(n+h_k)$ under the existence of a Landau-Siegel zero for $x$ in an interval that depends on the modulus of the character whose Dirichlet series corresponds to the Landau-Siegel zero. Our work constitutes an improvement over the previous related results of Germán and Kátai, Chinis, and Tao and Teräväinen.

math.NT↗

arXiv2024

Applying the Resonance Method to $\textrm{Re}\left(e^{-iθ}\logζ(σ+it)\right)$

We apply the resonance method to Montgomery's convolution formula for $\textrm{Re}\left(e^{-iθ}\logζ(σ+it)\right)$ in the strip $1/2 < σ< 1$. This gives new insight into maximal values of $\textrm{Re}\left(e^{-iθ}\logζ(σ+it)\right)$ for $t \in [T^β,T]$ for all $β\in (0,1)$ and real $θ$.

math.NT↗