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- W2895797911 abstract "Let $chi$ range over the $(p-1)/2$ even Dirichlet characters modulo a prime $p$ and denote by $theta (x,chi)$ the associated theta series. The asymptotic behaviour of the second and fourth moments proved by Louboutin and the author implies that there exists at least $ gg p/ log p$ characters such that the associated theta function does not vanish at a fixed point. Constructing a suitable mollifier, we improve this result and show that there exists at least $ gg p/ sqrt{log p}$ characters such that $theta(x,chi) neq 0$ for any $x>0$. We give similar results for odd Dirichlet characters mod $p$." @default.
- W2895797911 created "2018-10-26" @default.
- W2895797911 creator A5013542925 @default.
- W2895797911 date "2018-10-12" @default.
- W2895797911 modified "2023-09-27" @default.
- W2895797911 title "Non vanishing of theta functions and sets of small multiplicative energy" @default.
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