Generalizations of girstmair’s formulas

  • M. Hlrabayashi


In 1994 and 1995 GIRSTMAIR gave (relative) class number formulas for the imaginary quadratic field\(\mathbb{Q}(\sqrt { - p} )\), P an odd prime with p ≡ 3 (mod 4) and p ≥ 7, using the coefficients of the digit expression of 1/p and z/p, respectively, where z is an integer with 1 ≤ z ≤p - 1. We extend the formulas to an imaginary abelian number field.

Keywords and phrases

digit expression relative class number imaginary abelian number field determinant 


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Copyright information

© Mathematische Seminar 2005

Authors and Affiliations

  1. 1.Kanazawa Institute of TechnologyIshikawaJapan

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