On character sums with distances on the upper half plane over a finite field

  • Authors:

  • Nicholas M. Katz;Igor E. Shparlinski;Maosheng Xiong

  • Affiliations:

  • Department of Mathematics, Princeton University, Princeton, NJ 08544-1000, USA;Department of Computing, Macquarie University, Sydney, NSW 2109, Australia;Department of Mathematics, Pennsylvania State University, State College, PA 16802, USA

  • Venue:
  • Finite Fields and Their Applications
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

Abstract

For the finite field F"q of q elements (q odd) and a quadratic non-residue (that is, a non-square) @a@?F"q, we define the distance function@d(u+v@a,x+y@a)=(u-x)^2-@a(v-y)^2vy on the upper half plane H"q={x+y@a|x@?F"q,y@?F"q^*}@?F"q"^"2. For two sets E,F@?H"q with #E=E, #F=F and a non-trivial additive character @j on F"q, we give the following estimate|@?w@?E,z@?F@j(@d(w,z))|==E) is non-trivial if EF/q^2-~ as q-~.