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On the Convergence of Series of Reciprocals of Primes Related to the Fermat Numbers

✍ Scribed by Michal Křı́žek; Florian Luca; Lawrence Somer

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
158 KB
Volume
97
Category
Article
ISSN
0022-314X

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✦ Synopsis

We examine densities of several sets connected with the Fermat numbers F m ¼ 2 2 m þ 1: In particular, we prove that the series of reciprocals of all prime divisors of Fermat numbers is convergent. We also show that the series of reciprocals of elite primes is convergent.

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## Abstract Let \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$K/\mathbb {Q}$\end{document} be a finite Galois extension with the Galois group __G__, and let χ be a character of __G__ with the associated Artin __L__‐function __L__(__s__, χ) defined in ℜ(__s__) > 1 by t