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One-Level Density of Low-lying Zeros of Quadratic and Quartic Hecke $L$ -functions

  • Peng Gao (a1) and Liangyi Zhao (a2)

Abstract

In this paper we prove some one-level density results for the low-lying zeros of families of quadratic and quartic Hecke $L$ -functions of the Gaussian field. As corollaries, we deduce that at least 94.27% and 5%, respectively, of the members of the quadratic family and the quartic family do not vanish at the central point.

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Author P. G. was supported in part by NSFC grant 11871082, and author L. Z. was supported by FRG grant PS43707.

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One-Level Density of Low-lying Zeros of Quadratic and Quartic Hecke $L$ -functions

  • Peng Gao (a1) and Liangyi Zhao (a2)

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