## On the characteristic polynomial of the gross regulator matrix

Publication
, Journal Article

Dasgupta, S; Spiess, M

Published in: Transactions of the American Mathematical Society

January 1, 2019

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.

### Duke Scholars

## Published In

Transactions of the American Mathematical Society

## DOI

## EISSN

1088-6850

## ISSN

0002-9947

## Publication Date

January 1, 2019

## Volume

372

## Issue

2

## Start / End Page

803 / 827

## Related Subject Headings

- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics

### Citation

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Chicago

ICMJE

MLA

NLM

Dasgupta, S., & Spiess, M. (2019). On the characteristic polynomial of the gross regulator matrix.

*Transactions of the American Mathematical Society*,*372*(2), 803–827. https://doi.org/10.1090/tran/7393Dasgupta, S., and M. Spiess. “On the characteristic polynomial of the gross regulator matrix.”

*Transactions of the American Mathematical Society*372, no. 2 (January 1, 2019): 803–27. https://doi.org/10.1090/tran/7393.Dasgupta S, Spiess M. On the characteristic polynomial of the gross regulator matrix. Transactions of the American Mathematical Society. 2019 Jan 1;372(2):803–27.

Dasgupta, S., and M. Spiess. “On the characteristic polynomial of the gross regulator matrix.”

*Transactions of the American Mathematical Society*, vol. 372, no. 2, Jan. 2019, pp. 803–27.*Scopus*, doi:10.1090/tran/7393.Dasgupta S, Spiess M. On the characteristic polynomial of the gross regulator matrix. Transactions of the American Mathematical Society. 2019 Jan 1;372(2):803–827.

## Published In

Transactions of the American Mathematical Society

## DOI

## EISSN

1088-6850

## ISSN

0002-9947

## Publication Date

January 1, 2019

## Volume

372

## Issue

2

## Start / End Page

803 / 827

## Related Subject Headings

- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics