On the Correlation of Multiplicative and the Sum of Additive Arithmetic Functions (Memoirs of the American Mathematical Society)

Elliott, P. D. T. A.

ISBN 10: 0821825984 / ISBN 13: 9780821825983

Published by Amer Mathematical Society, 1994

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Bibliographic Details

• Title: On the Correlation of Multiplicative and the Sum of Additive Arithmetic Functions (Memoirs of the American Mathematical Society)
• Publisher: Amer Mathematical Society
• Publication Date: 1994
• Language: English
• ISBN 10: 0821825984
• ISBN 13: 9780821825983
• Binding: Paperback
• Condition: Like New
• Book Type: book

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Synopsis

This work applies stability properties of the dual of a certain arithmetic operator to study the correlation of multiplicative arithmetic functions. The literature of number theory contains very little concerning such correlations despite their direct connection with the problem of prime pairs and Goldbach's conjecture concerning the representation of even integers as the sum of two primes. Elliott aims for a result of wide uniformity under very weak hypotheses. The uniformity obtained here enables a comprehensive investigation of the value distribution of sums of additive arithmetic functions on distinct arithmetic progressions. The underlying argument, which Elliott calls the method of the stable dual, has received no unified account in the literature. A short overview of the method, with historical remarks, is presented. The principal results presented here are all new and currently beyond the reach of any other method.