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

Graduate Thesis Or Dissertation

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Citeable URL: https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/7d278w55k

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Attribute Name	Values
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 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 2 ≤ g ≤ 10.
License	All rights reserved
Resource Type	Dissertation
Date Available	2013-05-20T19:58:46+00:00
Date Issued	2013-04-25
Degree Level	Doctoral
Degree Name	Doctor of Philosophy (Ph.D.)
Degree Field	Mathematics
Degree Grantor	Oregon State University
Commencement Year	2013
Advisor	Schmidt, Thomas
Committee Member	Escher, Christine Swisher, Holly Xue, Lan Flahive, Mary
Academic Affiliation	Mathematics
Non-Academic Affiliation	Oregon State University. Graduate School
Subject	Rational points (Geometry) Jacobians Continued fractions Curves, Algebraic
Rights Statement	In Copyright
Publisher	Oregon State University
Peer Reviewed	No
Language	English [eng]
Replaces	http://hdl.handle.net/1957/38663

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