A note on the congruent distribution of the number of prime factors of natural numbers (Q2764666)
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scientific article; zbMATH DE number 1690803
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the congruent distribution of the number of prime factors of natural numbers |
scientific article; zbMATH DE number 1690803 |
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A note on the congruent distribution of the number of prime factors of natural numbers (English)
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11 June 2002
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congruent distribution modulo 3
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number of prime factors
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zeta function
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Riemann's hypothesis is, roughly speaking, the fact that the congruent distribution modulo 2 of the number of prime factors of natural numbers is uniform. In this paper, we investigate the congruent distribution modulo 3 of the number of prime factors of natural number, and show that the distribution can not be uniform. The main tool in the proof is a many valued zeta function. As an appendix, we also report some results obtained by computational experiments.
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