Student Number Theory Seminar

Owen Sharpe, University of Waterloo

Vaughan's Identity, Exponential Sums over Primes, and Exponential Sums with Additive Coefficients

Vaughan's Identity is a technique for summing sequences of the form f(n) Lambda(n), where Lambda(n) is the von Mangoldt function. We apply it to f(n) = e(alpha n) to obtain asymptotics for the sums of sequences of the form e(alpha p). Finally, we show an application to summing sequences of the form f(n) e(alpha n), where f is an additive function satisfying f(p) = 1 for all prime p.

MC 5479