Exponential sums with multiplicative coefficients (Q5906258)

Generalizing previous results of Daboussi, Delange and themselves, the authors prove that \(\sum_{n\leq x}f(n)e(t(n))=o(x)\) holds for every uniformly summable multiplicative arithmetical function f under the following assumption on the function t: for every K there is a finite set \({\mathcal P}\) of primes such that \(\sum_{p\in {\mathcal P}}1/p>K\) and \(\sum_{n\leq x}e(t(pn)-t(qn))=o(x)\) for all \(p,q\in {\mathcal P}\), \(p\neq q\).