Jacques Benatar

Polynomials with multiplicative coefficients, and related questions.

I will discuss some recent work, joint with Alon Nishry and Brad Rodgers, concerning the distribution of Dirichlet and trigonometric polynomials generated by multiplicative coefficients f(n). In the first part of the talk, we will explore some old and new results for deterministic sequences f(n) (Mobius, Legendre symbol, etc), stopping along our journey to marvel at a variety of wild and thorny conjectures. The second half of the talk will be devoted to Steinhaus random multiplicative coefficients f(n) = X(n). These considerations give rise to a couple of intriguing arithmetic problems.