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arXiv · 1801.06906

Summatory function of the number of prime factors

Xianchang Meng
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Abstract

We consider the summatory function of the number of prime factors for integers $\leq x$ over arithmetic progressions. Numerical experiments suggest that some arithmetic progressions consist more number of prime factors than others. Greg Martin conjectured that the difference of the summatory functions should attain a constant sign for all sufficiently large $x$. In this paper, we provide strong evidence for Greg Martin's conjecture. Moreover, we derive a general theorem for arithmetic functions from the Selberg class.

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Xianchang Meng. 2018-01-21. Summatory function of the number of prime factors. https://arxiv.org/abs/1801.06906

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