Transition Mean Values of Shifted Convolution Sums

Details Transition Mean Values of Shifted Convolution Sums Transition Mean Values of Shifted Convolution Sums

2011-11-29

arxiv.org/abs/1111.7010v1

Mathematics

Number Theory

14 pages

Scientific paper

Let f be a classical holomorphic cusp form for SL_2(Z) of weight k which is a normalized eigenfunction for the Hecke algebra, and let \lambda(n) be its eigenvalues. In this paper we study "shifted convolution sums" of the eigenvalues \lambda(n) after averaging over many shifts h and obtain asymptotic estimates. The result is somewhat surprising: one encounters a transition region depending on the ratio of the square of the length of the average over h to the length of the shifted convolution sum. The phenomenon is similar to that encountered by Conrey, Farmer and Soundararajan in their 2000 paper Transition Mean Values of Real Characters, and the connection of both results to Eisenstein series and multiple Dirichlet series is discussed.

Affiliated with

Also associated with

No associations

Rating

Transition Mean Values of Shifted Convolution Sums 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 Transition Mean Values of Shifted Convolution Sums, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Transition Mean Values of Shifted Convolution Sums will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-6617