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Variations on the Chebychev bias phenomenon

Introductory Workshop: Analytic Number Theory February 06, 2017 - February 10, 2017

February 10, 2017 (02:00 PM PST - 03:00 PM PST)
Speaker(s): Florent Jouve (Université de Bordeaux I)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Chebychev bias

  • elliptic curves

  • sums of arithmetic functions

  • arithmetic in relation to conjectures

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Abstract

Chebychev's bias, in its classical form, is the preponderance in ``most'' intervals [2,x] of primes that are 3 modulo 4 over primes that are 1 modulo 4. Recently many generalizations and variations on this phenomenon have been explored. We will highlight the role played by some wide open conjectures on L-functions in the study of Chebychev's bias. Our focus will be on analogues of Chebychev's question to elliptic curves. In the case where the base field is a function field (of a curve over a finite field) we will report on joint work with Cha and Fiorilli and explain how unconditional results can be obtained

Supplements
27980?type=thumb Jouve Notes 3.81 MB application/pdf Download
Video/Audio Files

Variations On The Chebychev Bias Phenomenon

H.264 Video 18-Jouve_a.mp4 499 MB video/mp4 rtsp://videos.msri.org/data/000/027/851/original/18-Jouve_a.mp4 Download
H.264 Video 18-Jouve_b.mp4 265 MB video/mp4 rtsp://videos.msri.org/data/000/027/852/original/18-Jouve_b.mp4 Download
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