Nonlinear exponential twists of the Liouville function : Open Mathematics

摘要

Let λ(n) be the Liouville function. We find a nontrivial upper bound for the sum $$sumlimits_{X leqslant n leqslant 2X} {lambda (n)e^{2pi ilpha sqrt n } } ,0 e lpha in mathbb{R}$$ The main tool we use is Vaughan’s identity for λ(n).