Ranks of matrices of logarithms of algebraic numbers II: The matrix coefficient conjecture
Publication
, Journal Article
Dasgupta, S; Kakde, M
Published in: Advances in Mathematics
March 1, 2026
Many questions in number theory concern the nonvanishing of determinants of square matrices of logarithms (complex or p -adic) of algebraic numbers. We present a new conjecture that states that if such a matrix has vanishing determinant, then after a rational change of basis on the left and right, it can be made to have a vanishing coefficient.
Duke Scholars
Published In
Advances in Mathematics
DOI
EISSN
1090-2082
ISSN
0001-8708
Publication Date
March 1, 2026
Volume
487
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4902 Mathematical physics
- 4901 Applied mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Dasgupta, S., & Kakde, M. (2026). Ranks of matrices of logarithms of algebraic numbers II: The matrix coefficient conjecture. Advances in Mathematics, 487. https://doi.org/10.1016/j.aim.2025.110753
Dasgupta, S., and M. Kakde. “Ranks of matrices of logarithms of algebraic numbers II: The matrix coefficient conjecture.” Advances in Mathematics 487 (March 1, 2026). https://doi.org/10.1016/j.aim.2025.110753.
Dasgupta S, Kakde M. Ranks of matrices of logarithms of algebraic numbers II: The matrix coefficient conjecture. Advances in Mathematics. 2026 Mar 1;487.
Dasgupta, S., and M. Kakde. “Ranks of matrices of logarithms of algebraic numbers II: The matrix coefficient conjecture.” Advances in Mathematics, vol. 487, Mar. 2026. Scopus, doi:10.1016/j.aim.2025.110753.
Dasgupta S, Kakde M. Ranks of matrices of logarithms of algebraic numbers II: The matrix coefficient conjecture. Advances in Mathematics. 2026 Mar 1;487.
Published In
Advances in Mathematics
DOI
EISSN
1090-2082
ISSN
0001-8708
Publication Date
March 1, 2026
Volume
487
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4902 Mathematical physics
- 4901 Applied mathematics