Uniformity of the Möbius function in F_q[t]

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Speaker: 
Lê Thái Hoàng
Institution: 
University of Mississippi
Time: 
Thu, 03/15/2018 - 3:00pm - 4:00pm
Host: 
Nathan Kaplan
Location: 
RH 306

The Möbius randomness principle states that the Möbius function μ does not correlate with simple or low complexity sequences F(n), that is, we have non-trivial bounds for sums ∑ μ(n) F(n).

By analogy between the integers and the ring F_q[t] of polynomials over a finite field F_q, we study this principle in the latter setting and expect that for f in F_q[t], μ(f)  does not correlate with low degree polynomials evaluated at the coefficients of f. In this talk, I will talk about our results in the linear and quadratic case. This is joint work with Pierre-Yves Bienvenu.