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Granville and Soundararajan have recently suggested that a general study of multiplicative functions could form the basis of analytic number theory without zeros of L-functions; this is the so-called pretentious view of analytic number theory. Here we study multiplicative functions which arise from the arithmetic of number fields. For each finite Galois extension K/ℚ, we construct a natural class of completely multiplicative functions whose values are dictated by Artin symbols, and we show that...
Given an integer base and a completely -additive arithmetic function taking integer values, we deduce an asymptotic expression for the counting function
under a mild restriction on the values of . When , the base sum of digits function, the integers counted by are the so-called base Niven numbers, and our result provides a generalization of the asymptotic known in that case.
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