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Analytic twists of modular forms. (English) Zbl 1440.11067
Summary: We investigate non-correlation of Fourier coefficients of Maass forms against a class of real oscillatory functions, in analogy to known results for Frobenius trace functions. We also establish an equidistribution result for twisted horocycles as a consequence of our non-correlation result.

11F30 Fourier coefficients of automorphic forms
11L05 Gauss and Kloosterman sums; generalizations
11L07 Estimates on exponential sums
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