2008/03/25 by Igor E. Shparlinski, I. E. Shparlinski, Shparlinski, I. E.
Mathematics · #11A07 #11L07 #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #math.NT #msc:11A07 #msc:11L07
paper · pdf · doi:10.48550/arxiv.0803.3487
openalex publication_date 2008/03/25 · arxiv created 2008/03/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a generalisation of the classical Lehmer problem about the parity distribution of an integer and its modular inverse. We use some known estimates of exponential sums to study a more general question of simultaneous distribution of the residues of any fixed number of negative and positive powers of integers in prescribed arithmetic progressions. In particular, we improve and generalise a recent result of Y. Yi and W. Zhang.