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Piatetski-Shapiro primes in arithmetic progressions

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Let \(([n^c])_{n=1}^\infty \) be the Piatetski-Shapiro sequences. In this paper, it is proved that there exist infinitely many Piatetski-Shapiro primes in arithmetic progressions for \(1<c<\frac{12}{11}\). Moreover, we also prove that there exist infinitely many Carmichael numbers composed entirely of primes from Piatetski-Shapiro sequences for \(1<c<\frac{344}{337}\). These two theorems constitute improvements upon the previous results of Baker et al. (Acta Arith 157(1):37–68, 2013).

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Acknowledgements

The authors would like to express the most sincere gratitude to the referee for his/her patience in refereeing this paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, People’s Republic of China

    Victor Zhenyu Guo

  2. Department of Mathematics, China University of Mining and Technology, Beijing, 100083, People’s Republic of China

    Jinjiang Li

  3. School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, People’s Republic of China

    Min Zhang

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  1. Victor Zhenyu Guo
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  2. Jinjiang Li
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  3. Min Zhang
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Correspondence to Jinjiang Li.

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The first author is supported by the National Natural Science Foundation of China (No. 11901447) and the Fundamental Research Funds for the Central Universities (No. xzy012021030). The second author is supported by the National Natural Science Foundation of China (Grant Nos. 11901566, 11971476, 12071238) and the Fundamental Research Funds for the Central Universities (Grant No. 2022YQLX05). The third author is supported by the National Natural Science Foundation of China (Grant Nos. 12001047, 11971476) and the Scientific Research Funds of Beijing Information Science and Technology University (Grant No. 2025035)

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Guo, V.Z., Li, J. & Zhang, M. Piatetski-Shapiro primes in arithmetic progressions. Ramanujan J 60, 677–692 (2023). https://doi.org/10.1007/s11139-022-00636-7

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  • DOI: https://doi.org/10.1007/s11139-022-00636-7

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