In 2017, Jakubec gave a formula for the relative class number of the pth cyclotomic field, p an odd prime, by using a determinant related to the multiplication theorem for Bernoulli polynomials. We generalize his formula to an imaginary abelian number field and also determine the sign of the formula, which he had not given. As a corollary, we also determine the sign in a formula of Carlitz and Olson.

relative class number, imaginary abelian number field, cyclotomic field, determinant.

Received: March 19, 2021; Accepted: April 12, 2021; Published: June 28, 2021

How to cite this article: Mikihito Hirabayashi, A generalization of Jakubec’s formula related to the multiplication theorem for Bernoulli polynomials, JP Journal of Algebra, Number Theory and Applications 51(1) (2021), 1-26. DOI: 10.17654/NT051010001

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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