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On the Correlation of Multiplicative and the Sum of Additive Arithmetic Functions : Memoirs of the American Mathematical Society - Peter D Elliott

On the Correlation of Multiplicative and the Sum of Additive Arithmetic Functions

Memoirs of the American Mathematical Society

Paperback Published: January 1994
ISBN: 9780821825983
Number Of Pages: 88

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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.

Correlations of multiplicative functions
The method of the stable dual (1): Deriving the approximate functional equations
The method of the stable dual (2): Solving the approximate functional equations
Orthogonality of operators and the present application of the method to the study of correlations
Correlations: Main lemma in the proof of theorem 1.1
Correlations: Auxiliary lemmas for the proof of theorem 1.1
Correlations: An approximate functional equation and its solution
Correlations: Proof of the main lemma (completion)
Correlations: Proof of theorem 1.1
Sums of additive functions
Afterwords: Further possibilities
References
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780821825983
ISBN-10: 0821825984
Series: Memoirs of the American Mathematical Society
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 88
Published: January 1994
Publisher: American Mathematical Society
Country of Publication: US
Dimensions (cm): 25.4 x 17.78  x 0.64
Weight (kg): 0.18

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