Skip to main content
Open Access Publications from the University of California


UCLA Electronic Theses and Dissertations bannerUCLA

Sums of SL(3,Z) Kloosterman Sums


We show that sums of the SL(3,Z) long element Kloosterman sum against a smooth weight function have cancellation due to the variation in argument of the Kloosterman sums, when each modulus is at least the square root of the other. Our main tool is Li's generalization of the Kuznetsov formula on SL(3,R), which has to date been prohibitively difficult to apply. We first obtain analytic expressions for the weight functions on the Kloosterman sum side by converting them to Mellin-Barnes integral form. This allows us to relax the conditions on the test function and to produce a partial inversion formula suitable for studying sums of the long-element SL(3,Z) Kloosterman sums.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View