On additive functions.
نویسندگان
چکیده
منابع مشابه
Additive Functions on Shifted Primes
Best possible bounds are obtained for the concentration function of an additive arithmetic function on sequences of shifted primes. A real-valued function / defined on the positive integers is additive if it satisfies f(rs) = f(r) + f(s) whenever r and s are coprime. Such functions are determined by their values on the prime-powers. For additive arithmetic function /, let Q denote the frequency...
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pα||n α. As usual p will denote primes, pα||n means that p divides n but p does not, and a function f(n) is additive if f(mn) = f(m)+f(n) whenever (m,n) = 1. From the pioneering works of Alladi and Erdős [1]-[2], P. Erdős’s perspicacity and insight have been one of the main driving forces in the research that brought on many results on summatory functions of large additive functions and P (n). ...
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The present paper deals with functions acting on the digits of an q-ary expansion. In particular let n be a positive integer, then we call
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Abstract. We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. The Kac-Kubilius model suggests that the distribution of values of a given additive function can be modeled by a sum of random variables. We show that the model is accurate when one is looking at values of the additive function around its mean...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1969
ISSN: 0026-2285
DOI: 10.1307/mmj/1029000316