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 language | English (US) |
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Pages (from-to) | 499-511 |
Number of pages | 13 |
Journal | Mathematische Zeitschrift |
Volume | 292 |
Issue number | 1-2 |
DOIs | |
State | Published - Jun 1 2019 |
Keywords
- Continued fractions
- Sondow’s Conjecture
- p-adic analytic functions
ASJC Scopus subject areas
- General Mathematics