The a-number of hyperelliptic curves

2017/03/10 by Sarah Frei, Frei, Sarah
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Cryptography and Residue Arithmetic

paper · pdf · doi:10.48550/arxiv.1703.03516

Abstract

It is known that for a smooth hyperelliptic curve to have a large a-number, the genus must be small relative to the characteristic of the field, p>0, over which the curve is defined. It was proven by Elkin that for a genus g hyperelliptic curve C to have a_C=g-1, the genus is bounded by g

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