Abstract
We present a practical polynomial-time algorithm for computing the zeta function of a Kummer curve over a finite field of small characteristic. Such algorithms have recently been obtained using a method of Kedlaya based upon Monsky–Washnitzer cohomology, and are of interest in cryptography. We take a different approach. The problem is reduced to that of computing the L-function of a multiplicative character sum. This latter task is achieved via a cohomological formula based upon the work of Dwork and Reich. We show, however, that our method and that of Kedlaya are very closely related.
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Communicated by Hendrik Lenstra
Dedicated to the memory of Gian-Carlo Rota
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Lauder, A. Computing Zeta Functions of Kummer Curves via Multiplicative Characters. Found Comput Math 3, 273–295 (2003). https://doi.org/10.1007/s10208-002-0066-6
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DOI: https://doi.org/10.1007/s10208-002-0066-6