3 results
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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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.
Vanishing of the μ-invariant of p-adic Hecke L-functions
- Part of
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- Journal:
- Compositio Mathematica / Volume 147 / Issue 4 / July 2011
- Published online by Cambridge University Press:
- 24 March 2011, pp. 1151-1178
- Print publication:
- July 2011
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Hecke
$L$-Functions and the Distribution of Totally Positive Integers
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- Journal:
- Canadian Journal of Mathematics / Volume 59 / Issue 4 / 01 August 2007
- Published online by Cambridge University Press:
- 20 November 2018, pp. 673-695
- Print publication:
- 01 August 2007
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Let
$K$ be a totally real number field of degree 
$n$. We show that the number of totally positive integers (or more generally the number of totally positive elements of a given fractional ideal) of given trace is evenly distributed around its expected value, which is obtained from geometric considerations. This result depends on unfolding an integral over a compact torus.
