Sondow’s conjecture, convergents to e, and p-adic analytic functions

Vicenţiu Paşol, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

Abstract

In their study of diophantine approximation of the exponential function in connection with Sondow’s Conjecture, Berndt et al. (Adv Math 348:1298–1331, 2013) have constructed certain p-adic functions arising from the sequence of convergents to the continued fraction of e. We solve an open problem posed in [2], more precisely we show that those p-adic functions are locally analytic (of minimal radius 1 / 2). We leave open the question of the existence of nontrivial zeros (i.e. zeros that are not forced by the functional equations) for these functions.

Original languageEnglish (US)
Pages (from-to)499-511
Number of pages13
JournalMathematische Zeitschrift
Volume292
Issue number1-2
DOIs
StatePublished - Jun 1 2019

Keywords

  • Continued fractions
  • Sondow’s Conjecture
  • p-adic analytic functions

ASJC Scopus subject areas

  • General Mathematics

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