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- W3215975330 abstract "Abstract We consider negative moments of quadratic Dirichlet $L$–functions over function fields. Summing over monic square-free polynomials of degree $2g+1$ in $mathbb{F}_{q}[x]$, we obtain an asymptotic formula for the $k^{textrm{th}}$ shifted negative moment of $L(1/2+beta ,chi _{D})$, in certain ranges of $beta $ (e.g., when roughly $beta gg log g/g $ and $k<1$). We also obtain non-trivial upper bounds for the $k^{textrm{th}}$ shifted negative moment when $log (1/beta ) ll log g$. Previously, almost sharp upper bounds were obtained in [ 3] in the range $beta gg g^{-frac{1}{2k}+epsilon }$." @default.
- W3215975330 created "2021-12-06" @default.
- W3215975330 creator A5038217519 @default.
- W3215975330 date "2023-06-15" @default.
- W3215975330 modified "2023-09-27" @default.
- W3215975330 title "Negative Moments of <i>L</i>–Functions With Small Shifts Over Function Fields" @default.
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- W3215975330 doi "https://doi.org/10.1093/imrn/rnad118" @default.
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