Varieties via their L-functions
Number Theory
2018-03-05 v2
Abstract
We describe a procedure for determining the existence, or non-existence, of an algebraic variety of a given conductor via an analytic calculation involving L-functions. The procedure assumes that the Hasse-Weil L-function of the variety satisfies its conjectured functional equation, but there is no assumption of an associated automorphic object or Galois representation. We demonstrate the method by finding the Hasse-Weil L-functions of all hyperelliptic curves of conductor less than 500.
Cite
@article{arxiv.1502.00850,
title = {Varieties via their L-functions},
author = {David W. Farmer and Sally Koutsoliotas and Stefan Lemurell},
journal= {arXiv preprint arXiv:1502.00850},
year = {2018}
}
Comments
14 pages, 2 figures