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Strong orthogonality between the Möbius function, additive characters and Fourier coefficients of cusp forms
- Part of
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- Journal:
- Compositio Mathematica / Volume 150 / Issue 5 / May 2014
- Published online by Cambridge University Press:
- 24 April 2014, pp. 763-797
- Print publication:
- May 2014
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- Article
- Export citation
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Let
$\nu _{f}(n)$ be the 
$n\mathrm{th}$ normalized Fourier coefficient of a Hecke–Maass cusp form 
$f$ for 
${\rm SL }(2,\mathbb{Z})$ and let 
$\alpha $ be a real number. We prove strong oscillations of the argument of 
$\nu _{f}(n)\mu (n) \exp (2\pi i n \alpha )$ as 
$n$ takes consecutive integral values.
