Lower order terms for expected value of traces of Frobenius of a family of cyclic covers of Pq 1 and one-level densities

Patrick Meisner

doi:10.1142/S1793042123500215

Lower order terms for expected value of traces of Frobenius of a family of cyclic covers of Pq 1 and one-level densities

Patrick Meisner^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the expected value of Tr(ΘCn) where C runs over a thin family of r-cyclic covers of Pq1 for any r. We obtain many lower order terms dependent on the divisors of r. We use these results to calculate the one-level density of the family and hypothesize a refined one-level density result.

Original language	English
Pages (from-to)	439-465
Number of pages	27
Journal	International Journal of Number Theory
Volume	19
Issue number	2
DOIs	https://doi.org/10.1142/S1793042123500215
State	Published - 1 Mar 2023
Externally published	Yes

Keywords

L -functions
distribution of zeroes
function fields
one-level density
random matrix theory

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10.1142/S1793042123500215

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abstract = "We consider the expected value of Tr(ΘCn) where C runs over a thin family of r-cyclic covers of Pq1 for any r. We obtain many lower order terms dependent on the divisors of r. We use these results to calculate the one-level density of the family and hypothesize a refined one-level density result.",

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AB - We consider the expected value of Tr(ΘCn) where C runs over a thin family of r-cyclic covers of Pq1 for any r. We obtain many lower order terms dependent on the divisors of r. We use these results to calculate the one-level density of the family and hypothesize a refined one-level density result.

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KW - distribution of zeroes

KW - function fields

KW - one-level density

KW - random matrix theory

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Lower order terms for expected value of traces of Frobenius of a family of cyclic covers of Pq 1 and one-level densities

Abstract

Keywords

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