| Title:
|
Bounds and computational results for exponential sums related to cusp forms (English) |
| Author:
|
Ernvall-Hytönen, Anne-Maria |
| Author:
|
Lepistö, Arto |
| Language:
|
English |
| Journal:
|
Acta Mathematica Universitatis Ostraviensis |
| ISSN:
|
1214-8148 |
| Volume:
|
17 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
81-90 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
cusp forms |
| Keyword:
|
exponential sums |
| Keyword:
|
Ramanujan tau function |
| Keyword:
|
analytic computations |
| MSC:
|
11L07 |
| MSC:
|
11Y35 |
| idZBL:
|
Zbl 1246.11138 |
| idMR:
|
MR2582961 |
| . |
| Date available:
|
2010-03-08T21:30:48Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137529 |
| . |
| Reference:
|
[1]
: PARI/GP, Version @vers.2006. available from http://pari.math.u-bordeaux.fr/ |
| Reference:
|
[2] Apostol, T. M.: Modular functions and Dirichlet series in number theory.volume 41 of Graduate Texts in Mathematics. Springer-Verlag, New York, second edition, 1990 Zbl 0697.10023, MR 1027834 |
| Reference:
|
[3] 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) |
| Reference:
|
[4] Ernvall-Hytönen, A.-M., Karppinen, K.: On short exponential sums involving Fourier coefficients of holomorphic cusp forms.IntṀath. Res. Not. IMRN, (10) : Art. ID. rnn022, 44, 2008 Zbl 1247.11106, MR 2429240 |
| Reference:
|
[5] Ernvall-Hytönen, A.-M.: An improvement on the upper bound of exponential sums of holomorphic cusp forms.submitted |
| Reference:
|
[6] Ivić, A.: Large values of certain number-theoretic error terms.Acta Arith., 56(2) : 135–159, 1990 MR 1075641 |
| Reference:
|
[7] Jutila, M.: On exponential sums involving the Ramanujan function.Proc. Indian Acad. Sci. Math. Sci., 97(1-3) : 157–166 (1988), 1987 MR 0983611 |
| Reference:
|
[8] Koecher, M., Krieg, A.: Elliptische Funktionen und Modulformen.Springer-Verlag, Berlin, 1998 Zbl 0895.11001, MR 1711085 |
| Reference:
|
[9] Rankin, R. A.: Contributions to the theory of Ramanujan’s function $\tau (n)$ and similar arithmetical functions ii. The order of Fourier coefficients of integral modular forms.Proc. Cambridge Philos. Soc., 35 : 357–372, 1939 |
| Reference:
|
[10] Wilton, J. R.: A note on Ramanujan’s arithmetical function $\tau (n)$.Proc. Cambridge Philos. Soc., 25(II) : 121–129, 1929 |
| . |
