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Memoirs of the American Mathematical Society
1994; 88 pp; softcover
List Price: US$37
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Order Code: MEMO/112/538
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.
Graduate students and researchers in number theory.
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