On multiplicative functions with mean-value close to −1 on primes.

Abstract In [5] , the first author and A. Sankaranarayanan established an upper bound for the sum ∑ n ≤ x f (n) , where f (n) is a multiplicative function for which the sum ∑ p ∈ I f (p) p − i t is small for certain intervals I. In this paper we consider functions f (p) , for which | ∑ p ∈ I f (p) p − i t + ∫ I u − i t log ⁡ u d u | is small. [ABSTRACT FROM AUTHOR]