Explicit asymptotics for certain single and double exponential sums

Abstract: By combining classical techniques together with two novel asymptotic identities contained in [FL], we analyse certain single sums of Riemann-zeta type. In addition, we analyse Euler-Zagier double exponential sums for particular values of $Re{u}$ and $Re{v}$ and for a variety of sets of summation, as well as particular cases of Mordell-Tornheim double sums. Some of these results are used in [F] where a novel approach to the Lindel\"of hypothesis is presented.