On integer values of Kloosterman sums

Abstract. In this note we use Carlitz's lifting formula for Kloosterman sums and some results from the theory of cyclotomic fields to show that a Kloosterman sum over a finite field obtains a rational integer value at a fixed point if and only if the same sum lifted to any extension field remains a rational integer.

• Type: Journal
• Year: 2010
• Where: TIT
• Authors: Keijo Petteri Kononen, Marko Juhani Rinta-Aho, Keijo O. Väänänen
• Keywords: Education, Kloosterman Sum, Rational Integer, Rational Integer Value, TIT 2010