Congruence function fields of genus 𝑔 and class number 𝑔+1

Leitzel, James R. C.

doi:10.1090/S0002-9939-1977-0437503-7

Congruence function fields of genus $g$ and class number $g+1$
HTML articles powered by AMS MathViewer

by James R. C. Leitzel PDF

Proc. Amer. Math. Soc. 64 (1977), 20-24 Request permission

Abstract:

Congruence function fields of genus g and class number $g + 1$ are fully classified. As an application we determine explicitly the real quadratic function fields with this property and of odd characteristic for which the ring of integers is a unique factorization domain.

References

E. Artin, Quadratische Körper im Gebiete der höheren Kongruenzen. I, Math. Z. 19 (1924), no. 1, 153–206 (German). MR 1544651, DOI 10.1007/BF01181074
Martin Eichler, Introduction to the theory of algebraic numbers and functions, Pure and Applied Mathematics, Vol. 23, Academic Press, New York-London, 1966. Translated from the German by George Striker. MR 0209258
Manohar L. Madan, Note on a problem of S. Chowla, J. Number Theory 2 (1970), 279–281. MR 268157, DOI 10.1016/0022-314X(70)90055-7
Manohar L. Madan and Clifford S. Queen, Algebraic function fields of class number one, Acta Arith. 20 (1972), 423–432. MR 306160, DOI 10.4064/aa-20-4-423-432
Manohar L. Madan and Daniel J. Madden, The exponent of class groups in congruence function fields, Acta Arith. 32 (1977), no. 2, 183–205. MR 439820, DOI 10.4064/aa-32-2-183-205
Friedrich Karl Schmidt, Analytische Zahlentheorie in Körpern der Charakteristik $p$, Math. Z. 33 (1931), no. 1, 1–32 (German). MR 1545199, DOI 10.1007/BF01174341