A note on the periodic $$L_2$$-discrepancy of Korobov’s p-sets
A note on the periodic $$L_2$$-discrepancy of Korobov’s p-sets
Abstract We study the periodic $$L_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> -discrepancy of point sets in the d -dimensional torus. This discrepancy is intimately connected with the root-mean-square $$L_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> -discrepancy of shifted point sets, with the notion of diaphony, and with the worst-case error of cubature formulas for the integration of …