On the characteristic polynomial of the gross regulator matrix

Journal Article (Journal Article)

We present a conjectural formula for the principal minors and the characteristic polynomial of Gross’s regulator matrix associated to a totally odd character of a totally real field. The formula is given in terms of the Eisenstein cocycle, which was defined and studied earlier by the authors and collaborators. For the determinant of the regulator matrix, our conjecture follows from recent work of Kakde, Ventullo, and the first author. For the diagonal entries, our conjecture overlaps with the conjectural formula presented in our prior work. The intermediate cases are new and provide a refinement of the Gross-Stark conjecture.

Full Text

Duke Authors

Cited Authors

  • Dasgupta, S; Spiess, M

Published Date

  • January 1, 2019

Published In

Volume / Issue

  • 372 / 2

Start / End Page

  • 803 - 827

Electronic International Standard Serial Number (EISSN)

  • 1088-6850

International Standard Serial Number (ISSN)

  • 0002-9947

Digital Object Identifier (DOI)

  • 10.1090/tran/7393

Citation Source

  • Scopus