ON THE RELATIVE ZETA FUNCTION IN FUNCTION FIELDS

다국어 초록 (Multilingual Abstract)

In the previous paper [8], the author gave a determinant formula of relative zeta function for cyclotomic function fields. Our purpose of this paper is to extend this result for more general function fields. As an application of our formula, we will give determinant formulas of class numbers for constant field extensions.

참고문헌 (Reference)

1 K. Girstmair, "The relative class numbers of imaginary cyclic fields of degrees 4, 6, 8, and 10" 61 (61): 881-887, 1993

2 M. Rosen, "Number Theory in Function Fields" Springer-Verlag 2002

3 L. Carlitz, "Maillet’s determinant" 6 : 265-269, 1955

4 K. Tateyama, "Maillet’s determinant" 32 (32): 97-100, 1982

5 L. C. Washington, "Introduction to Cyclotomic Fields" Springer-Verlag 1982

6 D. R. Hayes, "Explicit class field theory for rational function fields" 189 : 77-91, 1974

7 J. Ahn, "Class number formulae in the form of a product of determinants in function fields" 78 (78): 227-238, 2005

8 T. Mets¨ankyl¨a, "Bemerkungen ¨uber den ersten Faktor der Klassenzahl des Kreisk¨orpers" (105) : 15-, 1967

9 M. Rosen, "A note on the relative class number in function fields" 125 (125): 1299-1303, 1997

10 D. Shiomi, "A determinant formula for relative congruence zeta functions for cyclotomic function fields" 89 (89): 133-144, 2010