Euler’s divergent series in arithmetic progressions
Ernvall-Hytönen, Anne-Maria; Matala-aho, Tapani; Seppälä, Louna (2019-02-22)
Ernvall-Hytönen, Anne-Maria
Matala-aho, Tapani
Seppälä, Louna
University of Waterloo
22.02.2019
Ernvall-Hytönen, A-M., Matala-aho, T. & Seppälä, L. (2019) Euler’s divergent series in arithmetic progressions. Journal of integer sequences 22(2), article 19.2.2. https://cs.uwaterloo.ca/journals/JIS/VOL22/Seppala/seppala2.pdf
https://rightsstatements.org/vocab/InC/1.0/
© 2019 The Authors.
https://rightsstatements.org/vocab/InC/1.0/
© 2019 The Authors.
https://rightsstatements.org/vocab/InC/1.0/
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi-fe2020040710622
https://urn.fi/URN:NBN:fi-fe2020040710622
Tiivistelmä
Abstract
Let \(ξ\) and \(m\) be integers satisfying \(ξ \ne 0\) and \(m ≥ 3\). We show that for any given integers \(a\) and \(b\), \(b \ne 0\), there are \(\frac{φ(m)}{2}\) reduced residue classes modulo \(m\) each containing infinitely many primes \(p\) such that \(a−bF_p(ξ) \ne 0\), where \(F_p(ξ) =\sum^{\infty}_{n=0} n!ξ^n\) is the p-adic evaluation of Euler’s factorial series at the point \(ξ.\)
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