The influence of the first term of an arithmetic progression

Details The influence of the first term of an arithmetic progression The influence of the first term of an arithmetic progression

2011-04-13

arxiv.org/abs/1104.2542v1

Mathematics

Number Theory

51 pages

Scientific paper

The goal of this article is to study the discrepancy of the distribution of arithmetic sequences in arithmetic progressions. We will fix a sequence $\A=\{\a(n)\}_{n\geq 1}$ of non-negative real numbers in a certain class of arithmetic sequences. For a fixed integer $a\neq 0$, we will be interested in the behaviour of $\A$ over the arithmetic progressions $a \bmod q$, on average over $q$. Our main result is that for certain sequences of arithmetic interest, the value of $a$ has a significant influence on this distribution, even after removing the first term of the progressions.

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