On sums of Hecke series in short itervals

Details On sums of Hecke series in short itervals On sums of Hecke series in short itervals

2003-11-21

arxiv.org/abs/math/0311374v1

Journal de The\'eorie des Nombres de Bordeaux 13(2001), 453-468

Mathematics

Number Theory

16 pages

Scientific paper

We prove $\sum_{K-G}\le \kappa_j \le K+G}\alpha_j H_j^3(1/2) \ll_\epsilon GK^{1+\epsilon}$ for $K^\epsilon \le G \le K$, where $\alpha_j = |\rho_j(1)|^2(\cosh \pi\kappa_j)^{-1}$, and $\rho_j(1)$ is the first Fourier coefficient of the Maass wave form corresponding to the eigenvalue $\lambda_j = \kappa_j^2 + 1/4$ to which the Hecke series $H_j(s)$ is attached. This result yields the new bound $H_j(1/2) \ll_\epsilon \kappa_j^{1/3+\epsilon}$.

Affiliated with

Also associated with

No associations

Rating

On sums of Hecke series in short itervals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On sums of Hecke series in short itervals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On sums of Hecke series in short itervals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-112712