Event Type:

Ph.D.Defense

Date/Time:

Thursday, April 25, 2013 - 06:00

Location:

Valley Library 1420

Guest Speaker:

Abstract:

We use the theory of continued fractions over function fields in the setting of hyperelliptic

curves of equation y^2 = f(x); with deg(f) = 2g+2. By introducing a new sequence

of polynomials defined in terms of the partial quotients of the continued fraction expansion

of y, we are able to bound the sum of the degrees of consecutive partial quotients.

This allows us both (1) to improve the known naive upper bound for the order N of the

divisor at infinity on a hyperelliptic curve; and, (2) to apply a naive method to search for

hyperelliptic curves of given genus g and order N. In particular, we present new families

defined over Q with N = 11 and 1 <g < 11.

Host: