arXiv subjects

J. J. Rodríguez-Vega

Publications and source records attributed to J. J. Rodríguez-Vega.

3 recordsLinked to original sources

arXiv2024

Explicit formula in a imaginary quadratic number field

In \cite{Haran_1990}, Haran, using Riesz potentials, presents a version of the classical explicit formula for the Riemann zeta function that treats all places equally. In this article, we extend Haran's results to the case of an imaginary quadratic extension of $\mathbb{Q}$. To this end, we define Riesz kernels for both the totally ramified and complex cases. Although Haran implicitly addressed the unramified extension, we also include this case for the sake of completeness. Following Haran's approach with the Riemann zeta function, we demonstrate that these Riesz kernels naturally arise in connection with the contributions of the totally ramified and complex places to the Dedekind zeta function of the imaginary quadratic extension.

math.NT↗

arXiv2021

A new class of $p$-adic Lipschitz functions and multidimensional Hensel's Lemma

In this work we study $p$-adic continuous functions in several variables taking values on $\mathbb{Z}_p$. We describe the orthonormal van der Put base of these functions and study various Lipschitz conditions in several variables, generalizing previous work of Anashin. In particular, we introduce a new class of $p$-adic Lipschitz functions and study some of their properties. We also prove a Hensel's lifting lemma for this new class of functions, generalizing previous results of Yurova and Khrennikov.

math.NT↗

arXiv2018

P-adic Markov process and the problem of the first return over balls

Let $\langle x\rangle^α=(\max\{|x|_{p},p^r\})^α$ and $H^αφ=\mathcal{F}^{-1}[(\langle ξ\rangle^α -p^{rα})\mathcal{F}φ]$, in this article we study the Markov process associated to this operator and the first passage time problem associated to $H^α$.

math-ph↗