Thirteenth Algorithmic Number Theory Symposium ANTS-XIII University of Wisconsin, Madison July 16 – 20, 2018 Thirteenth Algorithmic Number Theory Symposium (ANTS-XIII) July 16 – 20, 2018

Cyclic extensions of prime degree and their p-adic regulators

Tommy Hofmann and Yinan Zhang

Abstract: We present a conjecture on the distribution of the valuations of p-adic regulators of cyclic extensions of Q of odd prime degree. This is based on the observation of computational data of p-adic regulators of the 5,521,222 cyclic quintic and 329,708 cyclic septic extensions of Q for 2 < p < 100 with discriminant up to 5 x 10³¹ and 10⁴² respectively, and noting that the observation matches the model that the entries in the regulator matrix are random elements with respect to the obvious restrictions.

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