Exponential sums with multiplicative coefficients without the Ramanujan conjecture

  title={Exponential sums with multiplicative coefficients without the Ramanujan conjecture},
  author={Yujiao Jiang and Guangshi L{\"u} and Zhiwei Wang},
  journal={Mathematische Annalen},
We study the exponential sum involving multiplicative function f under milder conditions on the range of f , which generalizes the work of Montgomery and Vaughan. As an application, we prove cancellation in the sum of additively twisted coefficients of automorphic L -function on $$\text {GL}_m$$ GL m $$(m\ge 4)$$ ( m ≥ 4 ) , uniformly in the additive character. 
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