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- W3204387178 abstract "Let $f in S_k(Gamma_1(N))$ be a primitive holomorphic form of arbitrary weight $k$ and level $N$. We show that the completed $L$-function of $f$ has $Omegaleft(T^deltaright)$ simple zeros with imaginary part in $left[-T, Tright]$, for any $delta < frac{2}{27}$. This is the first power bound in this problem for $f$ of non-trivial level, where previously the best results were $Omega(logloglog{T})$ for $N$ odd, due to Booker, Milinovich, and Ng, and infinitely many simple zeros for $N$ even, due to Booker. In addition, for $f$ of trivial level ($N=1$), we also improve an old result of Conrey and Ghosh on the number of simple zeros." @default.
- W3204387178 created "2021-10-11" @default.
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- W3204387178 date "2021-09-30" @default.
- W3204387178 modified "2023-09-27" @default.
- W3204387178 title "Simple zeros of $mathrm{GL}(2)$ $L$-functions" @default.
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