EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 86(100), pp. 97–105 (2009)

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A RELATION BETWEEN FOURIER COEFFICIENTS OF HOLOMORPHIC CUSP FORMS AND EXPONENTIAL SUMS

Anne-Maria Ernvall-Hytönen

Department of Mathematics, University of Turku, Turku, Finland

Abstract: 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.

Classification (MSC2000): 11L07; 11F11, 11F30

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