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Expected value of high powers of trace of frobenius of biquadratic curves over a finite field

Published online by Cambridge University Press:  22 April 2018

PATRICK MEISNER
PATRICK MEISNER*
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Tel Aviv, IL. e-mail: [email protected]
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Abstract

Denote ΘC as the Frobenius class of a curve C over the finite field 𝔽q. In this paper we determine the expected value of Tr(ΘCn) where C runs over all biquadratic curves when q is fixed and g tends to infinity. This extends work done by Rudnick [15] and Chinis [5] who separately looked at hyperelliptic curves and Bucur, Costa, David, Guerreiro and Lowry-Duda [1] who looked at ℓ-cyclic curves, for ℓ a prime, as well as cubic non-Galois curves.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 166 , Issue 3 , May 2019 , pp. 543 - 565
Copyright
Copyright © Cambridge Philosophical Society 2018 

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References

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