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Exponential sums involving the Möbius function

Volume 175 / 2016

Xiaoguang He, Bingrong Huang Acta Arithmetica 175 (2016), 201-209 MSC: 11L03, 11L20. DOI: 10.4064/aa8130-5-2016 Published online: 15 September 2016

Abstract

Let $\mu (n)$ be the Möbius function, and $e(x)=e^{2\pi ix}$ with $x$ real. We estimate exponential sums involving the Möbius function $$ S_k(x,\alpha )= \sum _{n\leq x}\mu (n)e(n^k\alpha ) $$ under the weak Generalized Riemann Hypothesis when $k\geq 3$.

Authors

  • Xiaoguang HeSchool of Mathematics
    Shandong University
    Jinan, Shandong 250100, China
    e-mail
  • Bingrong HuangSchool of Mathematics
    Shandong University
    Jinan, Shandong 250100, China
    e-mail

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