2 results
ONE-LEVEL DENSITY OF LOW-LYING ZEROS OF QUADRATIC HECKE L-FUNCTIONS OF IMAGINARY QUADRATIC NUMBER FIELDS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 112 / Issue 2 / April 2022
- Published online by Cambridge University Press:
- 29 October 2020, pp. 170-192
- Print publication:
- April 2022
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- Article
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In this paper, we prove a one level density result for the low-lying zeros of quadratic Hecke L-functions of imaginary quadratic number fields of class number 1. As a corollary, we deduce, essentially, that at least
$(19-\cot (1/4))/16 = 94.27\ldots \%$
of the L-functions under consideration do not vanish at 1/2.
One-Level Density of Low-lying Zeros of Quadratic and Quartic Hecke
$L$-functions
- Part of
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- Journal:
- Canadian Journal of Mathematics / Volume 72 / Issue 2 / April 2020
- Published online by Cambridge University Press:
- 30 August 2019, pp. 427-454
- Print publication:
- April 2020
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- Article
- Export citation
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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.
