Class numbers of real quadratic function fields

• Autorzy: Christian Friesen , Paul van Wamelen
• Języki publikacji: EN

Kategorie tematyczne

• 11R11: Quadratic extensions
• 11R29: Class numbers, class groups, discriminants
• 11R58: Arithmetic theory of algebraic function fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 81
• Numer: 1
• Strony: 45-55

Daty

wydano

1997

otrzymano

1996-05-17

poprawiono

1996-10-01

Twórcy

autor

Christian Friesen

• Ohio State University at Marion, 1465 Mt. Vernon Avenue, Marion, Ohio 43302, U.S.A.

autor

Paul van Wamelen

• Department of Mathematics, Louisiana State University, Baton Rogue, Louisiana 70803-4918, U.S.A.

Bibliografia

• [1] E. Artin, Quadratische Körper im Gebiet der höheren Kongruenzen I, II, Math. Z. 19 (1924), 153-246.
• [2] J. W. S. Cassels, Lectures on Elliptic Curves, London Math. Soc. Student Texts 24, Cambridge University Press, 1991.
• [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] M. Filaseta and O. Trifonov, On gaps between squarefree numbers. II, J. London Math. Soc. (2) 45 (1992), 215-221.
• [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] C. Friesen, Randomness of class groups of some real quadratic function fields, in preparation.
• [7] C. F. Gauss, Disquisitiones Arithmeticae, Yale University Press; A. A. Clarke, New Haven, Conn., 1966.
• [8] D. R. Hayes, Real quadratic function fields, in: CMS Conf. Proc. 7, 1985, 203-236.
• [9] D. Mumford, Tata Lectures on Theta II, Progr. Math. 43, Birkhäuser, 1984.
• [10] J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64-94.
• [11] T. A. Schmidt, Infinitely many real quadratic fields of class number one, J. Number Theory 54 (1995), 203-205.
• [12] R. Schoof, Nonsingular plane cubic curves over finite fields, J. Combin. Theory Ser. A 46 (1987), 183-211.
• [13] J. Tate, Endomorphisms of abelian varieties over finite fields, Invent. Math. 2 (1966), 134-144.
• [14] R. Warlimont, Squarefree numbers in arithmetic progressions, J. London Math. Soc. (2) 22 (1980), 21-24.
• [15] W. C. Waterhouse, Abelian varieties over finite fields, Ann. Sci. École Norm. Sup. (4) 2 (1969), 521-560.