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

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/7d278w55k

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  • 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.
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  • description.provenance : Submitted by Katthaleeya Daowsud (daowsudk@onid.orst.edu) on 2013-05-17T23:50:37Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: bb87e2fb4674c76d0d2e9ed07fbb9c86 (MD5) KatthaleeyaDaowsud2013.pdf: 457448 bytes, checksum: 29655797ab6809af4eb175e84601d49c (MD5)
  • description.provenance : Approved for entry into archive by Laura Wilson(laura.wilson@oregonstate.edu) on 2013-05-20T19:58:46Z (GMT) No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: bb87e2fb4674c76d0d2e9ed07fbb9c86 (MD5) KatthaleeyaDaowsud2013.pdf: 457448 bytes, checksum: 29655797ab6809af4eb175e84601d49c (MD5)
  • description.provenance : Approved for entry into archive by Julie Kurtz(julie.kurtz@oregonstate.edu) on 2013-05-20T18:33:52Z (GMT) No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: bb87e2fb4674c76d0d2e9ed07fbb9c86 (MD5) KatthaleeyaDaowsud2013.pdf: 457448 bytes, checksum: 29655797ab6809af4eb175e84601d49c (MD5)
  • description.provenance : Made available in DSpace on 2013-05-20T19:58:46Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: bb87e2fb4674c76d0d2e9ed07fbb9c86 (MD5) KatthaleeyaDaowsud2013.pdf: 457448 bytes, checksum: 29655797ab6809af4eb175e84601d49c (MD5) Previous issue date: 2013-04-25

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