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Continued fractions and the divisor at infinity on a hyperelliptic curve : examples and order bounds

Creator:

Daowsud, Katthaleeya

Abstract:

We use the theory of continued fractions over function fields in the setting of hyperelliptic curves of equation y²=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...

Resource Type:

Dissertation

Full Text:

2.2., we briefly review vocabulary of elementary algebraic geometry so as to define these terms. Our