Timeline for On periods of algebraic integers modulo rational primes
Current License: CC BY-SA 2.5
6 events
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| Feb 28, 2010 at 8:40 | history | edited | Pete L. Clark |
added tag (characteristic p)
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| Feb 7, 2010 at 9:48 | comment | added | Andrea Mori | Bjorn, thanks for your comment. I got the paper of Roskam quoted above by Ben together with a nice short paper of H.W. Lenstra (Séminaire Delange-Pisot-Poitou, 1977) and the 1967 paper of Hooley on the Artin's conjecture, and I somehow got convinced that any precise answer must use the Generalized Riemann Hypothesis. For the moment, I'll be happy to find just the right heuristics in the quadratic case toggling with the fields $K(\mu_n,\sqrt[n](\lambda),\sqrt[n](\bar{\lambda}))$ along the lines of Roskam. | |
| Feb 6, 2010 at 18:04 | comment | added | Bjorn Poonen | @Andrea: I suspect that this may be unknown even for K=Q, in which case one cannot expect an answer for higher number fields. | |
| Jan 30, 2010 at 20:21 | comment | added | Ben Weiss | This sounds like a little like a "smooth" version of Artin's Conjecture for number fields. If I'm correct in understanding that, try looking up Hans Roskam's work on the subject "Quadratic Analogue of Artin's Conjecture." | |
| Jan 30, 2010 at 14:45 | comment | added | Ben Weiss | Is another question which would imply yours: Are there infinitely many primes p so that p-1 is \ell smooth (meaning it is divisible by only primes less than \ell) | |
| Jan 30, 2010 at 13:33 | history | asked | Andrea Mori | CC BY-SA 2.5 |