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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
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
References
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