LOWER-ORDER TERMS OF THE ONE-LEVEL DENSITY OF A FAMILY OF QUADRATIC HECKE -FUNCTIONS

Peng Gao, Liangyi Zhao

Type: Article

Publication Date: 2022-02-22

Citations: 1

DOI: https://doi.org/10.1017/s1446788721000410

Abstract

Abstract In this paper, we study lower-order terms of the one-level density of low-lying zeros of quadratic Hecke L -functions in the Gaussian field. Assuming the generalized Riemann hypothesis, our result is valid for even test functions whose Fourier transforms are supported in $(-2, 2)$ . Moreover, we apply the ratios conjecture of L -functions to derive these lower-order terms as well. Up to the first lower-order term, we show that our results are consistent with each other when the Fourier transforms of the test functions are supported in $(-2, 2)$ .

Locations

Journal of the Australian Mathematical Society - View
arXiv (Cornell University) - View - PDF

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