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2 results

  • A DETERMINANT FORMULA FOR RELATIVE CONGRUENCE ZETA FUNCTIONS FOR CYCLOTOMIC FUNCTION FIELDS

  • Part of
  • DAISUKE SHIOMI
  • Journal:
    Journal of the Australian Mathematical Society / Volume 89 / Issue 1 / August 2010
    Published online by Cambridge University Press:
    15 July 2010, pp. 133-144
    Print publication:
    August 2010
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  • Rosen gave a determinant formula for relative class numbers for cyclotomic function fields, which may be regarded as an analogue of the classical Maillet determinant. In this paper, we give a determinant formula for relative congruence zeta functions for cyclotomic function fields. Our formula may be regarded as a generalization of the determinant formula for the relative class number.

  • Class number formulae in the form of a product of determinants in function fields

  • Part of
  • Jaehyun Ahn, Soyoung Choi, Hwanyup Jung
  • Journal:
    Journal of the Australian Mathematical Society / Volume 78 / Issue 2 / April 2005
    Published online by Cambridge University Press:
    09 April 2009, pp. 227-238
    Print publication:
    April 2005
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  • In this paper, we generalize the Kučera's group-determinant formulae to obtain the real and relative class number formulae of any subfield of cyclotomic function fields with arbitrary conductor in the form of a product of determinants. From these formulae, we generalize the relative class number formula of Rosen and Bae-Kang and obtain analogous results of Tsumura and Hirabayashi for an intermediate field in the tower of cyclotomic function fields with prime power conductor.