Talk

Graduate Student Number Theory Seminar, Rutgers University, Spring 2025

• Title: From Equidistribution to the Weyl Bound

• Abstract: How does the sequence e(a*n) distribute on the unit circle? Here we denote e(x) = exp(2*pi*i*x). Around 100 years ago, Weyl discovered they're Equidistributed in some sense, if "a" is irrational. A crucial tool is a good upper bound for certain Exponential Sums. Around 5 to 8 years after Weyl's result, Landau (crediting to Hardy and Littlewood) utilized such good bound to estimate the Riemann zeta function along the critical line, obtaining a good bound, called the Weyl bound. As a cute fact from this bound, we can always find a prime number in the interval [n^3, (n+1)^3] for all large enough n.