Bounds and computational results for exponential sums related to cusp forms
Anne-Maria Ernvall-Hytönen; Arto Lepistö
Acta Mathematica Universitatis Ostraviensis (2009)
- Volume: 17, Issue: 1, page 81-90
- ISSN: 1804-1388
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topErnvall-Hytönen, Anne-Maria, and Lepistö, Arto. "Bounds and computational results for exponential sums related to cusp forms." Acta Mathematica Universitatis Ostraviensis 17.1 (2009): 81-90. <http://eudml.org/doc/35199>.
@article{Ernvall2009,
abstract = {The aim of this paper is to present some computer data suggesting the correct size of bounds for exponential sums of Fourier coefficients of holomorphic cusp forms.},
author = {Ernvall-Hytönen, Anne-Maria, Lepistö, Arto},
journal = {Acta Mathematica Universitatis Ostraviensis},
keywords = {cusp forms; exponential sums; Ramanujan tau function; analytic computations; cusp forms; exponential sums; Ramanujan tau function; analytic computations},
language = {eng},
number = {1},
pages = {81-90},
publisher = {University of Ostrava},
title = {Bounds and computational results for exponential sums related to cusp forms},
url = {http://eudml.org/doc/35199},
volume = {17},
year = {2009},
}
TY - JOUR
AU - Ernvall-Hytönen, Anne-Maria
AU - Lepistö, Arto
TI - Bounds and computational results for exponential sums related to cusp forms
JO - Acta Mathematica Universitatis Ostraviensis
PY - 2009
PB - University of Ostrava
VL - 17
IS - 1
SP - 81
EP - 90
AB - The aim of this paper is to present some computer data suggesting the correct size of bounds for exponential sums of Fourier coefficients of holomorphic cusp forms.
LA - eng
KW - cusp forms; exponential sums; Ramanujan tau function; analytic computations; cusp forms; exponential sums; Ramanujan tau function; analytic computations
UR - http://eudml.org/doc/35199
ER -
References
top- PARI/GP, Version @vers, 2006. available from http://pari.math.u-bordeaux.fr/ (2006)
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- Ernvall-Hytönen, A.-M., A relation between Fourier coefficients of holomorphic cusp forms and exponential sums, to appear in Publications de l’Institut Mathematique (Beograd)
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- Ernvall-Hytönen, A.-M., An improvement on the upper bound of exponential sums of holomorphic cusp forms, submitted
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- Jutila, M., On exponential sums involving the Ramanujan function, Proc. Indian Acad. Sci. Math. Sci., 97(1-3) : 157–166 (1988), 1987 (1988) MR0983611
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- Rankin, R. A., Contributions to the theory of Ramanujan’s function and similar arithmetical functions ii. The order of Fourier coefficients of integral modular forms, Proc. Cambridge Philos. Soc., 35 : 357–372, 1939 (1939)
- Wilton, J. R., A note on Ramanujan’s arithmetical function , Proc. Cambridge Philos. Soc., 25(II) : 121–129, 1929 (1929)
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