# A problem of Chowla and approximations by signed harmonic sums

Date(s) : 24/04/2018
11 h 00 min - 12 h 00 min

We discuss the non-vanishing of Dirichlet series of the form $\sum_n f(n)d_k(n)/n^s$
at the point s=1, where f is a periodic function modulo q.
We then give a few results concerning the quality of the approximation of a real number \tau by sums of the form \sum_{n\leq N} c_n /n with c_n\in\{\pm1\}, as N goes to infinity.

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