Academic Journal
Squares in a Beatty sequence and an improvement on character sums
| Title: | Squares in a Beatty sequence and an improvement on character sums |
|---|---|
| Authors: | Victor Z. Guo, Jinyun Qi, Mengyao Jing |
| Source: | The Ramanujan Journal. 66 |
| Publisher Information: | Springer Science and Business Media LLC, 2024. |
| Publication Year: | 2024 |
| Subject Terms: | Prime Number Theory and L-Functions, Algebra and Number Theory, Character (mathematics), Erdos-Rényi Random Graphs, Statistics, Latin Squares, Arithmetic Progressions, Geometry, Limits and Structures in Graph Theory, Hypergraphs, 16. Peace & justice, Optical Code Division Multiple Access, Engineering, Combinatorics, FOS: Biological sciences, Physical Sciences, FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, Genetics, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering, Biology, Mathematics, Coherent and Incoherent Systems, Sequence (biology) |
| Description: | We consider the distribution of perfect squares in a Beatty sequence, which is of the form ⌊αn + β⌋. We also analyze it on average over positive square-free integers. The proof relies on a new bound of character sums with Beatty sequences, which answers an open question posted by Igor Shparlinski. MSC Numbers: 11B83; 11L07; 11L40. |
| Document Type: | Article Other literature type |
| Language: | English |
| ISSN: | 1572-9303 1382-4090 |
| DOI: | 10.1007/s11139-024-00998-0 |
| DOI: | 10.21203/rs.3.rs-4322039/v1 |
| DOI: | 10.60692/wrrpf-rxk41 |
| DOI: | 10.60692/cy0fr-gv059 |
| Rights: | Springer Nature TDM CC BY |
| Accession Number: | edsair.doi.dedup.....21e90d58c7b57ca3b63d6d1bbeea024f |
| Database: | OpenAIRE |
| ISSN: | 15729303 13824090 |
|---|---|
| DOI: | 10.1007/s11139-024-00998-0 |