Article ID Journal Published Year Pages File Type
4594839 Journal of Number Theory 2010 19 Pages PDF
Abstract

For any positive integer m we obtain the asymptotic formula,|B∩V′|=|B′|ϕ(m)+O(8ν(m)τ(m)(logm)3(loglogm)7|B|), for the number of solutions of the congruence x1x2≡x3x4(modm) with coordinates relatively prime to m   in a box BB of arbitrary size and position. We also obtain an upper bound for a fourth-order character sum moment,1ϕ(m)∑χ≠χ0|∑x=a+1a+Bχ(x)|4≪8ν(m)τ(m)(logm)3(loglogm)7B2.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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