In this paper we study the upper bound for the absolute value of the exponential sum related to the Möbius function unconditionally and present some interesting applications also.
H. Maier;A. Sankaranarayanan, 2009, On certain exponential sums over primes, Journal of Number Theory, 129, 7, pp. 1669-1677, 10.1016/j.jnt.2009.01.018.