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The value distribution of additive arithmetic functions on a line
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P. D. T. A. Elliott
Published/Copyright:
February 9, 2010
Abstract
A stability study of the correlations of multiplicative arithmetic functions yields necessary and sufficient conditions that the frequency distributions naturally attached to sums of additive arithmetic functions ƒ1(n) + ƒ2(N – n) on the integers not exceeding N possess a limiting distribution as N traverses the positive integers, or the positive primes. Moreover, the functions ƒj may be allowed a wide class of unbounded renormalizations.
Received: 2007-04-10
Revised: 2008-12-17
Published Online: 2010-02-09
Published in Print: 2010-May
© Walter de Gruyter Berlin · New York 2010
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- On the Rosenberg-Zelinsky sequence in abelian monoidal categories
- Arakelov theory of noncommutative arithmetic surfaces
- The value distribution of additive arithmetic functions on a line
- Kähler-Ricci solitons on homogeneous toric bundles
- The Jiang–Su algebra revisited
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Articles in the same Issue
- On the Rosenberg-Zelinsky sequence in abelian monoidal categories
- Arakelov theory of noncommutative arithmetic surfaces
- The value distribution of additive arithmetic functions on a line
- Kähler-Ricci solitons on homogeneous toric bundles
- The Jiang–Su algebra revisited
- Trees of definable sets over the p-adics
- A new series of compact minitwistor spaces and Moishezon twistor spaces over them
