On the $p$-adic meromorphy of the function field height zeta function

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127932In this brief note, we will investigate the number of points of bounded (twisted) height in a projective variety defined over a function field, where the function field comes from a projective variety of dimension greater than or equal to 2. A first step in this investigation is to understand the $p$-adic analytic properties of the height zeta function. In particular, we will show that for a large class of projective varieties this function is $p$-adic meromorphic.5 pages. Comments welcomeNumber TheoryAlgebraic Geometry11G25; 11G50On the $p$-adic meromorphy of the function field height zeta functiontext