Wieferich past and future

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Scopus citations

Abstract

Let p be an odd prime. Wieferich related the question of whether 2p−1 − 1 is divisible by p2 to (the “first case” of) Fermat’s Last theorem for the exponent p. Here we formulate an equidistribution conjecture about the sequence, indexed by odd primes p, of fractions 2p-1-1/p2 mod ℤ in ℝ/ℤ. We then formulate versions of this conjecture for algebraic tori, for elliptic curves, for abelian varieties and for semi-abelian varieties.

Original languageEnglish (US)
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages253-270
Number of pages18
DOIs
StatePublished - 2015

Publication series

NameContemporary Mathematics
Volume632
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Abelian variety
  • Elliptic curve
  • Equidistribution
  • Groupscheme

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