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

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 app...

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Bibliographic Details
Published in:Journal of the Australian Mathematical Society (2001) 2023-04, Vol.114 (2), p.178-221
Main Authors: GAO, PENG, ZHAO, LIANGYI
Format: Article
Language:English
Subjects:
Density
Eigenvalues
Fourier transforms
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Summary: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 $(-2, 2)$ .
ISSN:1446-7887
1446-8107
DOI:10.1017/S1446788721000410