Mean value of Kloosterman sums over short intervals

Abstract

This paper is concerned with a kind of mean value problem of Kloosterman sums, which will lead to a sum of Kloosterman sums over short intervals.

Keywords

Mean value / Kloosterman sum / Short intervals

References

[1] Kloosterman H. D.. On the representation of numbers in the form ax ² +by ² +cz ²+dt ². Acta. Math., 1926, 49: 407-464

[2] Salié H.. Über die Kloostermanschen summen S(u, v; q). Math. Z., 1931, 34: 91-109