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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.

Published Paper
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© 2017-2018 Jennifer Paulhus (with thanks to Kiran S. Kedlaya, and by extension Pierrick Gaudry and Emmanuel Thomé)