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Note on a Paper by G. J. Rieger
Author(s) -
Hensley Doug
Publication year - 1996
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19961790107
Subject(s) - mathematics , combinatorics , image (mathematics) , artificial intelligence , computer science
Abstract 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 ).