Non-residues and primitive roots in Beatty sequences

DOI10.1017/S0004972700035449zbMath1144.11064OpenAlexW2101193774MaRDI QIDQ5480148

William D. Banks, Igor E. Shparlinski

Publication date: 26 July 2006

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972700035449

zbMATH Keywords

character sumsBeatty sequences

Mathematics Subject Classification ID

Special sequences and polynomials (11B83) Estimates on character sums (11L40) Distribution modulo one (11J71)

Related Items (12)

Kloosterman sums with twice-differentiable functions ⋮ Prime divisors in Beatty sequences ⋮ Consecutive quadratic residues and primitive roots in the sequences formed by twice-differentiable functions ⋮ k-Free numbers and integer parts of αp ⋮ Consecutive quadratic residues in Beatty sequences ⋮ АКТУАЛЬНЫЕ ЗАДАЧИ, СВЯЗАННЫЕ С ПОСЛЕДОВАТЕЛЬНОСТЯМИ БИТТИ ⋮ Kloosterman sums with Beatty sequences and application ⋮ Exponential sums with Piatetski-Shapiro sequences and their application to modular hyperbolas ⋮ Bilinear character sums over elliptic curves ⋮ Modular hyperbolas and Beatty sequences ⋮ On the distribution of Kloosterman sums ⋮ Metric results on summatory arithmetic functions on Beatty sets

Cites Work

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• A generating function technique for Beatty sequences and other step sequences
• Gap problems for integer part and fractional part sequences
• Estimates for the number of sums and products and for exponential sums over subgroups in fields of prime order.
• On the least pair of consecutive quadratic non-residues
• The fractional part of \(n\theta + \phi\) and Beatty sequences
• New bounds for Gauss sums derived from KTH powers, and for Heilbronn's exponential sum

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