Class numbers of real quadratic function fields

Christian Friesen; Paul van Wamelen

Acta Arithmetica (1997)

  • Volume: 81, Issue: 1, page 45-55
  • ISSN: 0065-1036

How to cite

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Christian Friesen, and Paul van Wamelen. "Class numbers of real quadratic function fields." Acta Arithmetica 81.1 (1997): 45-55. <http://eudml.org/doc/207054>.

@article{ChristianFriesen1997,
author = {Christian Friesen, Paul van Wamelen},
journal = {Acta Arithmetica},
keywords = {class numbers; functions fields; elliptic curves; Gauss conjecture; monic irreducible quartics},
language = {eng},
number = {1},
pages = {45-55},
title = {Class numbers of real quadratic function fields},
url = {http://eudml.org/doc/207054},
volume = {81},
year = {1997},
}

TY - JOUR
AU - Christian Friesen
AU - Paul van Wamelen
TI - Class numbers of real quadratic function fields
JO - Acta Arithmetica
PY - 1997
VL - 81
IS - 1
SP - 45
EP - 55
LA - eng
KW - class numbers; functions fields; elliptic curves; Gauss conjecture; monic irreducible quartics
UR - http://eudml.org/doc/207054
ER -

References

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  1. [1] E. Artin, Quadratische Körper im Gebiet der höheren Kongruenzen I, II, Math. Z. 19 (1924), 153-246. Zbl50.0107.01
  2. [2] J. W. S. Cassels, Lectures on Elliptic Curves, London Math. Soc. Student Texts 24, Cambridge University Press, 1991. 
  3. [3] H. Cohen and H. W. Lenstra, Jr., Heuristics on class groups of number fields, in: Number Theory Noordwijkerhout, H. Jager (ed.), Lecture Notes in Math. 1068, Springer, Berlin, 1984, 33-62. 
  4. [4] M. Filaseta and O. Trifonov, On gaps between squarefree numbers. II, J. London Math. Soc. (2) 45 (1992), 215-221. 
  5. [5] E. Friedman and L. C. Washington, On the distribution of divisor class groups of curves over a finite field, in: Théorie des nombres (Québec, PQ, 1987), de Gruyter, Berlin, 1989, 227-239. 
  6. [6] C. Friesen, Randomness of class groups of some real quadratic function fields, in preparation. 
  7. [7] C. F. Gauss, Disquisitiones Arithmeticae, Yale University Press; A. A. Clarke, New Haven, Conn., 1966. 
  8. [8] D. R. Hayes, Real quadratic function fields, in: CMS Conf. Proc. 7, 1985, 203-236. 
  9. [9] D. Mumford, Tata Lectures on Theta II, Progr. Math. 43, Birkhäuser, 1984. Zbl0549.14014
  10. [10] J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64-94. Zbl0122.05001
  11. [11] T. A. Schmidt, Infinitely many real quadratic fields of class number one, J. Number Theory 54 (1995), 203-205. Zbl0839.11053
  12. [12] R. Schoof, Nonsingular plane cubic curves over finite fields, J. Combin. Theory Ser. A 46 (1987), 183-211. Zbl0632.14021
  13. [13] J. Tate, Endomorphisms of abelian varieties over finite fields, Invent. Math. 2 (1966), 134-144. Zbl0147.20303
  14. [14] R. Warlimont, Squarefree numbers in arithmetic progressions, J. London Math. Soc. (2) 22 (1980), 21-24. Zbl0444.10036
  15. [15] W. C. Waterhouse, Abelian varieties over finite fields, Ann. Sci. École Norm. Sup. (4) 2 (1969), 521-560. Zbl0188.53001

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