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- W2013434269 abstract "Mean-value theorems with sharp quantitative remainder term estimates and theorems on the distribution of values are proved for a large class of multiplicative functions. This class is characterized by the existence of an abscissa of absolute convergence ≤ 1 for the Dirichlet series of the quotient f ˜ ( s ) / ζ ( s ) , where f ˜ ( s ) is the Dirichlet series associated with ƒ and ζ( s ) denotes the Riemann zeta function. In particular, the mean behaviour of ƒ on certain sequences a , namely, that of Mersenne numbers 2 n −1 and that of shifted primes p −1 with natural n and prime p , respectively, is studied and cluster points of the image sequence f(a) of a are determined. The strength of the results is demonstrated by new results for some specific functions." @default.
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- W2013434269 date "2004-12-01" @default.
- W2013434269 modified "2023-09-30" @default.
- W2013434269 title "Mean behaviour and distribution properties of multiplicative functions" @default.
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- W2013434269 doi "https://doi.org/10.1016/j.camwa.2004.01.015" @default.
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