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

2007/04/25 by C. Douglas Haessig, Haessig, C. Douglas
Mathematics · #11G25 #11G50 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11G25 #msc:11G50

paper · pdf · doi:10.48550/arxiv.0704.3410

5 pages. Comments welcome

arxiv created 2007/04/25 · arxiv updated 2009/12/01

Abstract

In 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.

Related

• Counting rational points on Hirzebruch-Kleinschmidt varieties over global function fields
• On the zeta function of divisors for projective varieties with higher rank divisor class group
• Height zeta functions of projective bundles
• Computing zeta functions via p-adic cohomology
• Fonction zêta des hauteurs des variétés toriques non déployées