Generalization of the Von Staudt-Clausen theorem

Date
1989
Authors
Dibag, I.
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Source Title
Journal of Algebra
Print ISSN
0021-8693
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Publisher
Elsevier
Volume
125
Issue
2
Pages
519 - 523
Language
English
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Abstract

The localization LS(x) of log(1 + x) at a set of primes S is defined by taking those powers of x in the logarithmic series for log(1 + x) which lie in the span of S. The functional inverse LS-1(x) of LS(x) also localizes the functional inverse ex - 1 of log(1 + x) and a generalization of the Von Staudt-Clausen theorem is proved for the even coefficients in the power series expansion for x LS-1(x). This reduces to the Von Staudt-Clausen theorem when S is the set of all primes and to a weaker version of Theorem 3.9 of I. Dibag (J. Algebra87 (1984), 332-341) when S consists of a single prime. © 1989.

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