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Varieties via their L-functions

Journal article
Authors D. W. Farmer
S. Koutsoliotas
Stefan Lemurell
Published in Journal of Number Theory
Volume 196
Pages 364-380
ISSN 0022-314X
Publication year 2019
Published at Department of Mathematical Sciences
Pages 364-380
Language en
Keywords Degree 4, Functional equation, Hasse–Weil L-function, L-function
Subject categories Algebra and Logic


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, with 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. © 2018 Elsevier Inc.

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