Bounds and computational results for exponential sums related to cusp forms

 Access to full text

 Full (PDF)

1. PARI/GP, Version @vers, 2006. available from http://pari.math.u-bordeaux.fr/ (2006) 
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 (1990) Zbl0697.10023MR1027834
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) 
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 (2008) Zbl1247.11106MR2429240
5. Ernvall-Hytönen, A.-M., An improvement on the upper bound of exponential sums of holomorphic cusp forms, submitted 
6. Ivić, A., Large values of certain number-theoretic error terms, Acta Arith., 56(2) : 135–159, 1990 (1990) MR1075641
7. Jutila, M., On exponential sums involving the Ramanujan function, Proc. Indian Acad. Sci. Math. Sci., 97(1-3) : 157–166 (1988), 1987 (1988) MR0983611
8. Koecher, M., Krieg, A., Elliptische Funktionen und Modulformen, Springer-Verlag, Berlin, 1998 (1998) Zbl0895.11001MR1711085
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 (1939) 
10. Wilton, J. R., A note on Ramanujan’s arithmetical function $\tau (n)$, Proc. Cambridge Philos. Soc., 25(II) : 121–129, 1929 (1929)