Abstract
We investigate the distribution of integers with a fixed number of prime factors in arithmetic progressions, and obtain a generalization of the Siegel–Walfisz theorem under the extended Riemann hypothesis. As an application, we consider a problem of P. Erdős, A. M. Odlyzko and A. Sárközy about the representation of residue classes modulo q by products of two integers with a fixed number of prime factors. We show some conditional results.
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This research is partially supported by Project 973 (No. 2013CB834205) and the science and technology foundation of the ministry of education (No. 210123) and Shandong provincial natural science foundation (No. ZR2013AM006) in China.
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Meng, X.M. A Generalization of the Siegel–Walfisz Theorem and its Application. Acta Math. Hungar. 143, 491–501 (2014). https://doi.org/10.1007/s10474-014-0400-x
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DOI: https://doi.org/10.1007/s10474-014-0400-x