Mathematics at OSU Marion


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Mathematical Research of Dr. Chris Friesen

Algebraic and Computational Number Theory: continued fractions and class group structure in quadratic function fields.

A selection of recent papers:

  1. Friesen, Christian Bounds for frequencies of class groups of real quadratic genus 1 function fields. Acta Arith. 96 (2001), no. 4, 313--331.
  2. Friesen, Christian Class group frequencies of real quadratic function fields: the degree 4 case. Math. Comp. 69 (2000), no. 231, 1213--1228.
  3. Friesen, Christian A special case of Cohen-Lenstra heuristics in function fields. Number theory (Ottawa, ON, 1996), 99--105, CRM Proc. Lecture Notes, 19, Amer. Math. Soc., Providence, RI, 1999.
  4. Friesen, Christian; van Wamelen, Paul Class numbers of real quadratic function fields. Acta Arith. 81 (1997), no. 1, 45--55.
  5. Friesen, Christian; Hensley, Doug The statistics of continued fractions for polynomials over a finite field. Proc. Amer. Math. Soc. 124 (1996), no. 9, 2661--2673.
  6. Friesen, C. Continued fraction characterization and generic ideals in real quadratic function fields. The arithmetic of function fields (Columbus, OH, 1991), 465--474, Ohio State Univ. Math. Res. Inst. Publ., 2, de Gruyter, Berlin, 1992.
  7. Friesen, Christian Class number divisibility in real quadratic function fields. Canad. Math. Bull. 35 (1992), no. 3, 361--370.
  8. Friesen, Christian Legendre symbols and continued fractions. Acta Arith. 59 (1991), no. 4, 365--379.
  9. Friesen, Christian On continued fractions of given period. Proc. Amer. Math. Soc. 103 (1988), no. 1, 9--14.
  10. Friesen, Christian; Muskat, Joseph B.; Spearman, Blair K.; Williams, Kenneth S. Cyclotomy of order $15$ over ${\rm GF}(p\sp 2), p=4, 11({\rm mod}\,15)$. Internat. J. Math. Math. Sci. 9 (1986), no. 4, 665--704.
  11. Friesen, C.; Spearman, B. K.; Williams, K. S. Another proof of Eisenstein's law of cubic reciprocity and its supplement. Rocky Mountain J. Math. 16 (1986), no. 2, 395--402.
  12. Williams, Kenneth S.; Hardy, Kenneth; Friesen, Christian On the evaluation of the Legendre symbol $((A+B\sqrt m)/p)$. Acta Arith. 45 (1985), no. 3, 255--272.
  13. Williams, Kenneth S.; Friesen, Christian; Howe, Lawrence J. Criteria for biquadratic residuacity modulo a prime $p$ involving quaternary representations of $p$. Canad. J. Math. 37 (1985), no. 2, 337--370.
  14. Williams, Kenneth S.; Friesen, Christian Remark on the class number of $Q(\sqrt{2p})$ modulo $8$ for $p\equiv 5\;({\rm mod}\,8)$ a prime. Proc. Amer. Math. Soc. 93 (1985), no. 2, 198--200.