On the Chevalley-Bass number of a field
Jean Gillibert, Florence Gillibert, Gabriele Ranieri
TL;DR
This paper establishes bounds and provides an algorithm for computing the Chevalley-Bass number of characteristic zero fields, with applications to exponential Diophantine equations.
Contribution
It introduces new bounds and an algorithm for the Chevalley-Bass number, enhancing understanding and computation of this invariant in number theory.
Findings
Derived upper and lower bounds for the Chevalley-Bass number.
Developed an algorithm to compute the Chevalley-Bass number given the maximal abelian subextension.
Improved the constant related to exponential Diophantine equations.
Abstract
We give upper and lower bounds on the Chevalley-Bass number of a field of characteristic zero, whenever this quantity is well-defined. We also describe an algorithm which computes the Chevalley-Bass number of a field, provided its maximal abelian subextension is known. As a primary application, we improve the value of a constant related to exponential diophantine equations.
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