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

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

2007-04-25

arxiv.org/abs/0704.3410v1

Mathematics

Number Theory

5 pages. Comments welcome

Scientific paper

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.

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