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An arithmetic progression is a (possibly infinite) sequence of numbers such that the difference between consecutive terms is always the same value.

5 votes
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Remainder terms of congruence sums in sets of positive density

Let $\mathcal A$ be the set of all $n\in \mathbb N$ with a prime factor $p>\sqrt{n}$. First, the number of elements $a\in \mathcal A$ with $a\leq x$ is $\gg x$. Indeed, this large prime factor is uni …
Alexander Kalmynin's user avatar
19 votes
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Are there any papers about this observation of the distribution of the zeros of the zeta fun...

This is called Landau's formula. More precisely, if we extend the von Mangoldt function $\Lambda(n)$ to the function $\Lambda:\mathbb R_+\to \mathbb R$ by $\Lambda(x)=0$ for non-integer $x$, then $$ \ …
Alexander Kalmynin's user avatar