JP Journal of Algebra, Number Theory and Applications
Volume 38, Issue 2, Pages 151 - 184
(April 2016) http://dx.doi.org/10.17654/NT038020151 |
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ON SOME GENERALIZATIONS OF MEAN VALUE THEOREMS FOR ARITHMETIC FUNCTIONS OF TWO VARIABLES
Noboru Ushiroya
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Abstract: Let be an arithmetic function of two variables. We study the existence of the limit:
where kis a fixed positive integer. Moreover, we express this limit as an infinite product over all prime numbers in the case that fis a multiplicative function of two variables. This study is a generalization of Cohen-van der Corput’s results to the case of two variables. |
Keywords and phrases: asymptotic results, arithmetic functions. |
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