Computing $L$-functions with large conductor

Details Computing $L$-functions with large conductor Computing $L$-functions with large conductor

2003-06-05

arxiv.org/abs/math/0306101v3

Mathematics

Number Theory

Latex; 15 pages, 4 figures. To appear in Mathematics of Computation. Title changed at referee's request

Scientific paper

An algorithm is given to efficiently compute $L$-functions with large
conductor in a restricted range of the critical strip. Examples are included
for about 21000 dihedral Galois representations with conductor near $10^7$. The
data shows good agreement with a symplectic random matrix model. Also included
are an elliptic curve $L$-function and one for a quadratic Dirichlet character.

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