Quantum computation of zeta functions of curves

Kiran S. Kedlaya

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Quantum computation of zeta functions of curves

Kiran S. Kedlaya

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Abstract

We exhibit a quantum algorithm for determining the zeta function of a genus g curve over a finite field F_q, which is polynomial in g and log(q). This amounts to giving an algorithm to produce provably random elements of the class group of a curve, plus a recipe for recovering a Weil polynomial from enough of its cyclic resultants. The latter effectivizes a result of Fried in a restricted setting.

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BibTeX RIS

Kiran S. Kedlaya. 2005-11-30. Quantum computation of zeta functions of curves. https://arxiv.org/abs/math/0411623

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