Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter March 25, 2015

A Generalization of Jakubec's Formula

  • Mikihito Hirabayashi EMAIL logo
From the journal Mathematica Slovaca

Abstract

In 2009 Jakubec gave two determinantal formulas for the relative class number of the pth cyclotomic field, p an odd prime. We generalize one of the formulas to an arbitrary cyclotomic field and also determine the sign of the formula, which he had not given.

References

[1] HASSE, H.: Über die Klassenzahl abelscher Zahlkörper, Akademie-Verlag, Berlin, 1952; Springer, Berlin-Heidelberg-New York-Tokyo, 1985.10.1515/9783112471388Search in Google Scholar

[2] HIRABAYASHI, M.: A relative class number formula for an imaginary abelian number field by means of Demjanenko matrix. In: Proceedings of the Conference on Analytic and Elementary Number Theory (Vienna 1996), Vienna, 1997, pp. 81-91.Search in Google Scholar

[3] JAKUBEC, S.: On some new estimates for h−(Q(ζ)), Acta Arith. 137 (2009), 43-50.10.4064/aa137-1-2Search in Google Scholar

[4] METÄNKYLÄ, T.: Some divisibility results for the cyclotomic class number, Tatra Mt. Math. Publ. 11 (1997), 59-68.Search in Google Scholar

[5] WANG, K.: On Maillet determinant, J. Number Theory 18 (1984), 306-312.10.1016/0022-314X(84)90064-7Search in Google Scholar

[6] WASHINGTON, L. C.: Introduction to Cyclotomic Fields (2nd ed.), Springer, New York- Berlin-Heidelberg, 1997. 10.1007/978-1-4612-1934-7Search in Google Scholar

Received: 2012-7-12
Accepted: 2012-9-11
Published Online: 2015-3-25
Published in Print: 2015-2-1

© 2015 Mathematical Institute Slovak Academy of Sciences

Downloaded on 1.5.2024 from https://www.degruyter.com/document/doi/10.1515/ms-2015-0018/html
Scroll to top button