Lower Order Terms for Expected Value of Traces of Frobenius of a Family\n of Cyclic Covers of \ℙ¹_ mathbbF_q and One-Level Densities

2020/06/30 by Patrick Meisner, Meisner, Patrick · 1 citation
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Approximation and Integration #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2006.16886

openalex publication_date 2020/06/30 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We consider the expected value of \Tr(\Θ_Cⁿ) where C runs over\na thin family of r-cyclic covers of \ℙ¹_ mathbbF_q for any\nr. We obtain many lower order terms dependent on the divisors of r. We use\nthese results to calculate the one-level density of the family and hypothesize\na refined one-level density result.\n

Cited by

• Local Statistics for Zeros of Artin-Schreier L-functions

Related

• Expected Value of High Powers of Trace of Frobenius of Biquadratic\n Curves Over a Finite Field
• Statistics for biquadratic covers of the projective line over finite fields
• Traces, high powers and one level density for families of curves over finite fields
• On the distribution of traces of Frobenius for families of elliptic curves and the Lang-Trotter conjecture on average
• Note on the Distribution of the Traces of Frobenius