On irregularities of sums of integers

TL;DRAbstract

Benedek Valk (Budapest) 1. Introduction. Let A {1, . . . , N } and = |A|/N . In If the sequence n, n + q, . . . , n + (k -1)q has t elements in {1, . . . , N } then it is reasonable to think that a well-distributed sequence would have "about" t elements in this sequence if k is "big enough" relative to N . Thus if we set

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