Arithmetic combinatorics on Vinogradov systems
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Abstract:
In this paper, we present a variant of the Balog–Szemerédi–Gowers theorem for the Vinogradov system. We then use our result to deduce a higher degree analogue of the sum-product phenomenon.References
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Additional Information
- Akshat Mudgal
- Affiliation: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907-2067; and School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol, BS8 1UG, United Kingdom
- MR Author ID: 1341480
- Email: am16393@bristol.ac.uk; amudgal@purdue.edu
- Received by editor(s): July 26, 2019
- Received by editor(s) in revised form: November 2, 2019
- Published electronically: May 26, 2020
- Additional Notes: The author’s work is supported by a studentship sponsored by a European Research Council Advanced Grant under the European Union’s Horizon 2020 research and innovation programme via grant agreement No. 695223.
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 5491-5516
- MSC (2010): Primary 11B30, 11P99
- DOI: https://doi.org/10.1090/tran/8121
- MathSciNet review: 4127884