BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lucile Devin (Université du Littoral Côte d'Opale) DTSTART:20230531T150000Z DTEND:20230531T160000Z DTSTAMP:20260418T065523Z UID:LNTS/101 DESCRIPTION:Title: E xceptional biases (in the distribution of irreducible polynomials over fin ite fields)\nby Lucile Devin (Université du Littoral Côte d'Opale) a s part of London number theory seminar\n\nLecture held in KCL\, Strand Bui lding\, Room S3.30.\n\nAbstract\nStudying the secondary terms of the Prime Number Theorem in Arithmetic Progressions\, Chebyshev claimed that there are more prime numbers congruent to 3 modulo 4 than to 1 modulo 4. This cl aim was later corrected by Littlewood\, explained\, and quantified by Rubi nstein and Sarnak.\nPursuing the work of Cha\, we investigate analogues to Chebyshev's bias in the setting of irreducible polynomials over finite fi elds. In particular\, we observe exceptional behaviors occurring when the zeros of the involved L-functions are not linearly independent. More preci sely\, we will present instances of "complete bias" and "reversed bias"\, and explain why they occur with probability tending to 0\, in the large q limit.\n\nThis is joint work with Bailleul\, Keliher and Li.\n LOCATION:https://researchseminars.org/talk/LNTS/101/ END:VEVENT END:VCALENDAR