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On the error term in the approximate functional equation for exponential sums related to cusp forms. (English) Zbl 1251.11025

##### MSC:
 11F11 Holomorphic modular forms of integral weight 11F30 Fourier coefficients of automorphic forms 11F66 Langlands $$L$$-functions; one variable Dirichlet series and functional equations 11L07 Estimates on exponential sums
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##### References:
 [1] Ernvall-Hytönen A.-M., Int. Math. Res. Not. 2008 pp 44– [2] Jutila M., J. Reine Angew. Math. 355 pp 173– [3] Jutila M., Tata Institute of Fundamental Research Lectures on Mathematics and Physics 80, in: Lectures on a Method in the Theory of Exponential Sums (1987) [4] DOI: 10.1007/BF02837820 · Zbl 0658.10043 · doi:10.1007/BF02837820 [5] DOI: 10.1007/BF02588051 · Zbl 1098.11034 · doi:10.1007/BF02588051 [6] Lebedev N. N., Special Functions and Their Applications (1972) · Zbl 0271.33001 [7] DOI: 10.1017/S0305004100021101 · doi:10.1017/S0305004100021101 [8] Titchmarsh E. C., The Theory of the Riemann Zeta-Function (1951) · Zbl 0042.07901 [9] Wilton J. R., J. Reine Angew. Math. 169 pp 219–
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