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arXiv · 2408.08178

Ranks of Matrices of Logarithms of Algebraic Numbers II: The Matrix Coefficient Conjecture

Samit Dasgupta·Mahesh Kakde
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Abstract

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.

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Samit Dasgupta, Mahesh Kakde. 2024-08-15. Ranks of Matrices of Logarithms of Algebraic Numbers II: The Matrix Coefficient Conjecture. https://arxiv.org/abs/2408.08178

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