Álvaro Serrano Holgado

collaborators

4 papers

math.NT2023

A connection between the poles of the zeta function of a recurrence sequence and the module of relations of its roots

Álvaro Serrano Holgado

Answering a question left open in previous research, we study the enumeration of poles of the zeta function $φ (s)$ associated to an integer linear recurrence sequence ${a_{n}}$ . Th…

math.AG2023

Kummer theory over the geometric adeles of an algebraic curve

Luis Manuel Navas Vicente, Francisco J. Plaza Martín, Álvaro Serrano Holgado

Our goal is to give a purely algebraic characterization of finite abelian Galois covers of a complete, irreducible, non-singular curve $X$ over an algebraically closed field $\k$.…

math.NT2023

The Lerch-type zeta function of a recurrence sequence of arbitrary degree

Álvaro Serrano Holgado, Luis Manuel Navas Vicente

We consider the series $\sum_{n = 1}^{\infty} z^{n} (a_{n} + x)^{- s}$ where $a_{n}$ satisfies a linear recurrence of arbitrary degree with integer coefficients. Under appropriate con…

math.NT2023

The zeta function of a recurrence sequence of arbitrary degree

Álvaro Serrano Holgado, Luis Manuel Navas Vicente

We consider a Dirichlet series $\sum_{n = 1}^{\infty} a_{n}^{- s}$ , where $a_{n}$ satisfies a linear recurrence of arbitrary degree with integer coefficients. Under suitable hypotheses, we…