Note on a Paper by G. J. Rieger

Let c ε IN. For d ε ℤ with gcd ( d , c) = 1 let δ( d , c ) be defined by d · δ(d, c) 1 mod c , 1 ⩽ δ( d , c) ⩽ c . Let s , t ε IN with 1 ⩽ s ⩽ c , 1 ⩽ t ⩽ c . The main result is that for arbitrary fixed ε > 0, but uniformly over c, s and tEquivalently, the points ( d , δ( c , d )) are approximately uniformly distributed in [0, c] × [0, c ]: The two‐dimensional discrepancy of {( d ,δ ( c , d )): 1 ⩽ d ⩽ c and ( c , d )= 1} in [0,c] × [0,c] is Oε(c ε‐1 / 2 ).