Session S09 - Number Theory in the Americas

Thursday, July 22, 16:00 ~ 16:30 UTC-3

Unconditional discriminant lower bounds exploiting violations of the Generalized Riemann Hypothesis

Eduardo Friedman

U. Chile, Chile   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In the 1970's Andrew Odlyzko proved good lower bounds for the discriminant of a number field. He also showed that his results could be sharpened by assuming the Generalized Riemann Hypothesis. Some years later Odlyzko suggested that it might be possible to do without GRH. I shall explain Odlyzko's ideas and sketch how for number fields of reasonably small degree (say up to degree 11 or 12) one can indeed improve the lower known bounds by exploiting hypothetical violations of GRH. Our method extends unpublished results of Matias Atria.

Joint work with Karim Belabas (U. Bordeaux, France) and Francisco Diaz y Diaz (U. Bordeaux, France).

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