On the difference of consecutive numbers prime to n
C. Hooley (1963)
Acta Arithmetica
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C. Hooley (1963)
Acta Arithmetica
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B. Srinivasan (1963)
Acta Arithmetica
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R. Sitaramachandrarao (1987)
Acta Arithmetica
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H. Kesten (1964)
Acta Arithmetica
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Michael Drmota, Johannes Gajdosik (1998)
Journal de théorie des nombres de Bordeaux
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By using a generating function approach it is shown that the sum-of-digits function (related to specific finite and infinite linear recurrences) satisfies a central limit theorem. Additionally a local limit theorem is derived.
Franciszek Czekała (1996)
Applicationes Mathematicae
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The paper is concerned with the asymptotic normality of a certain statistic based on the logarithms of disjoint m-spacings. The exact and asymptotic mean and variance are computed in the case of uniform distribution on the interval [0,1]. This result is generalized to the case when the sample is drawn from a distribution with positive step density on [0,1].
Catalina Calderón García, María José Zárate Azcuna (1990)
Extracta Mathematicae
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W. K. A. Loh (1996)
Acta Arithmetica
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K. Chandrasekharan, H. Joris (1973)
Acta Arithmetica
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