Linear and quadratic uniformity of the Möbius function over $\mathbb{F}_q[t]$
Người báo cáo: Le Thai Hoang (University of Mississippi)

Thời gian: 9h Thứ 4, ngày 20/12/2017

Địa điểm: Phòng 611-612 Tầng 6 Nhà A6

Tóm tắt: The Möbius function $mu(n)$ is an important function in number theory and combinatorics. It is intimately linked with the distribution of primes. The Möbius randomness principle states that $mu$ is so random-like that it does not correlate with any bounded ``reasonable'' or ``low-complexity'' function $F$, in the sense that $sum_{nleq x}mu(n)F(n)=o(x)$. I will talk about an instance of this principle in $mathbb{F}_q[t]$ (the ring of polynomials over a finite field $mathbb{F}_q$), where $mu$ is replaced by its $mathbb{F}_q[t]$-counterpart and $F$ is a quadratic or linear phase. In the linear case our result is unconditional while in the quadratic case our result is conditional.
This is joint work with Pierre-Yves Bienvenu.


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