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A relation betwen Fourier coefficients of holomorphic cusp forms and exponential sums. (English) Zbl 1279.11083
Summary: We consider certain specific exponential sums related to holomorphic cusp forms, give a reformulation for the Lehmer conjecture and prove that certain exponential sums of Fourier coefficients of holomorphic cusp forms contain information on other similar non-overlapping exponential sums. Also, we prove an Omega result for short sums of Fourier coefficients.

##### MSC:
 11L07 Estimates on exponential sums 11F11 Holomorphic modular forms of integral weight 11F30 Fourier coefficients of automorphic forms
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