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- W4205959603 abstract "Abstract We establish a result of Bombieri–Vinogradov type for the Dirichlet coefficients at prime ideals of the standard $L$-function associated to a self-dual cuspidal automorphic representation $pi $ of $operatorname {GL}_n$ over a number field $F$ when $pi$ is not a quadratic twist of itself. Our result does not rely on any unproven progress towards the generalized Ramanujan conjecture or the nonexistence of Landau–Siegel zeros. In particular, when $pi $ is fixed and not equal to a quadratic twist of itself, we prove the first unconditional Siegel-type lower bound for the twisted $L$-values $|L(1,pi otimes chi )|$ in the $chi $-aspect, where $chi $ is a primitive quadratic Hecke character over $F$. Our result improves the levels of distribution in other works that relied on these unproven hypotheses. As applications, when $n=2,3,4$, we prove a $textrm {GL}_n$ analogue of the Titchmarsh divisor problem and a nontrivial bound for a certain $textrm {GL}_ntimes textrm {GL}_2$ shifted convolution sum." @default.
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- W4205959603 date "2021-10-04" @default.
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- W4205959603 title "A Bombieri–Vinogradov Theorem for Higher-Rank Groups" @default.
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- W4205959603 doi "https://doi.org/10.1093/imrn/rnab261" @default.
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