Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 385-395

MEAN SQUARE ESTIMATE FOR RELATIVELY SHORT EXPONENTIAL SUMS INVOLVING FOURIER COEFFICIENTS OF CUSP FORMS

Anne-Maria Ernvall-Hytönen

University of Helsinki, Department of Mathematics and Statistics
P.O. Box 68, FI-00014 University of Helsinki, Finland; anne-maria.ernvall-hytonen 'at' helsinki.fi

Abstract. We estimate the mean square of a short exponential sum involving Fourier coefficients of a cusp form with a linear twist, a smooth weight function, and a relatively short averaging interval.

2010 Mathematics Subject Classification: Primary 11L07, 11F11, 11F30.

Key words: Fourier coefficients, cusp forms, exponential sums, mean square.

Reference to this article: A.-M. Ernvall-Hytönen: Mean square estimate for relatively short exponential sums involving Fourier coefficients of cusp forms. Ann. Acad. Sci. Fenn. Math. 40 (2015), 385-395.

Full document as PDF file

doi:10.5186/aasfm.2015.4019