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Mathematische Zeitschrift

, Volume 292, Issue 1–2, pp 499–511 | Cite as

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

  • Vicenţiu PaşolEmail author
  • Alexandru Zaharescu
Article
  • 9 Downloads

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.

Keywords

Sondow’s Conjecture Continued fractions p-adic analytic functions 

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Simion Stoilow Institute of Mathematics of the Romanian AcademyBucharestRomania
  2. 2.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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