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arXiv · 2207.02378

On primes in special sequences with applications to Carmichael numbers

Wei Zhang
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Abstract

By involving some exponential sums related to $\Lambda(n)$ in arithmetic progression, we can obtain some new results for von Mangoldt function over {\bf nonhomogeneous} Beatty sequences in arithmetic progressions, which improve some recent results of Banks-Yeager unconditionally. On the other hand, we also considered the primes over Piatetski-Shapiro sequences in arithmetic progressions, which gives a continuous improvement of the results of \cite{BBB}. These results can be used to improve some results related to the Carmichael numbers.

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Wei Zhang. 2022-07-06. On primes in special sequences with applications to Carmichael numbers. https://arxiv.org/abs/2207.02378

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