We determine how big an Euler product can be at $s_2$, when its size at $s_1$ is known, and apply this via Halász's method to bound the mean value of a multiplicative function in terms of the size of the generating Dirichlet series.
"Local variation of Euler products." Funct. Approx. Comment. Math. 39 (2) 273 - 288, December 2008. https://doi.org/10.7169/facm/1229696576