Sums of $L$-functions over the rational function field

Details Sums of $L$-functions over the rational function field Sums of $L$-functions over the rational function field

2007-06-19

arxiv.org/abs/0706.2735v1

Mathematics

Number Theory

13 pages

Scientific paper

Friedberg, Hoffstein and Lieman have constructed two related multiple Dirichlet series from quadratic and higher-order $L$-functions and Gauss sums. We compute these multiple Dirichlet series explicitly in the case of the rational function field. This is done by utilizing the functional equation of the $L$-functions and the functional equation relating the two multiple Dirichlet series. We also point out a very simple correspondence between these series and their $p$-parts.

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