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

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## 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

## References

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