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Product of an integer free of small prime factors and prime in arithmetic progression

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Abstract

We establish estimates for the number of ways to represent any reduced residue class as a product of a prime and an integer free of small prime factors. Our best results is conditional on the Generalised Riemann hypothesis (GRH). As a corollary, we make progress on a conjecture of Erdös, Odlyzko, and Sárközy.

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Acknowledgements

The author thanks I. E. Shparlinski and L. Zhao for helpful comments. This work is supported by an Australian Government Research Training Program (RTP) Scholarship, UNSW PhD Writing Scholarship, and the Lift-off Fellowship of AustMS. The author is also grateful to the referee for their excellent comments which improved the presentation of the article.

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  1. Department of Pure Mathematics, University of New South Wales, Sydney, NSW, 2052, Australia

    Kam Hung Yau

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  1. Kam Hung Yau
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Correspondence to Kam Hung Yau.

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Communicated by Adrian Constantin.

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Yau, K.H. Product of an integer free of small prime factors and prime in arithmetic progression. Monatsh Math 196, 411–428 (2021). https://doi.org/10.1007/s00605-021-01606-9

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  • DOI: https://doi.org/10.1007/s00605-021-01606-9

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