@inbook{41dad18ef585467b8fa487ee9aac6e3b,

title = "Wieferich past and future",

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{\textquoteright}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.",

keywords = "Abelian variety, Elliptic curve, Equidistribution, Groupscheme",

author = "Katz, {Nicholas M.}",

note = "Publisher Copyright: {\textcopyright} 2015 American Mathematical Society.",

year = "2015",

doi = "10.1090/conm/632/12632",

language = "English (US)",

series = "Contemporary Mathematics",

publisher = "American Mathematical Society",

pages = "253--270",

booktitle = "Contemporary Mathematics",

address = "United States",

}