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Sebastian Pauli

Publications and source records attributed to Sebastian Pauli.

10 recordsLinked to original sources
arXiv2025

Families of p-adic fields

We improve the database of $p$-adic fields in the LMFDB by systematically using Krasner-Monge polynomials and working relatively as well as absolutely. These improvements organize $p$-adic fields into families. They thereby make long lists of fields more manageable and various theoretical structures more evident. In particular, the database now includes all degree $n$ extensions of $\mathbb{Q}_p$, for $p<200$ and $n \leq 23$.

math.NT↗
arXiv2023

Zeros of high derivatives of the Riemann Zeta function

The main aim of this paper is twofold. First we generalize, in a novel way, most of the known non-vanishing results for the derivatives of the Riemann zeta function by establishing the existence of an infinite sequence of regions in the right half-plane where these derivatives cannot have any zeros; and then, in the rare regions of the complex plane that do contain zeros of the k-th derivative of the zeta function, we describe a unexpected phenomenon, which implies great regularities in their zero distributions. In particular, we prove sharp estimates for the number of zeros in each of these new critical strips, and we explain how they converge, in a very precise, periodic fashion, to their central, critical lines, as k increases. This not only shows that the zeros are not randomly scattered to the right of the line Re(s)=1, but that, in many respects, their two-dimensional distribution eventually becomes much simpler and more predictable than the one-dimensional behavior of the zeros of the zeta function on the line Re(s)=1/2.

math.NT↗
arXiv2023

A Bound for Stieltjes Constants

The goal of this note is to improve on the currently available bounds for Stieltjes constants using the method of steepest descent applied by Coffey and Knessl to approximate Stieltjes constants.

math.NT↗
arXiv2023

Zeros of fractional derivatives of polynomials

We investigate the behavior of fractional derivatives of polynomials. In particular, we consider the locations and the asymptotic behaviour of their zeros and give bounds for their Mahler measure.

math.GM↗
arXiv2015

Enumerating Extensions of $(π)$-Adic Fields with Given Invariants

We give an algorithm that constructs a minimal set of polynomials defining all extension of a $(π)$-adic field with given, inertia degree, ramification index, discriminant, ramification polygon, and residual polynomials of the segments of the ramification polygon.

math.NT↗