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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

Variations On The Chebychev Bias Phenomenon

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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