Abstract
AbstractWe prove a variant of a square function estimate for the extension operator associated to the moment curve in non-archimedean local fields. The arguments rely on a structural analysis of congruences (sublevel sets) of univariate polynomials over field extensions of the base field. Our analysis can be adapted to the archimedean setting as well.
Publisher
Springer Science and Business Media LLC
Reference17 articles.
1. Biggs, K.D., Brandes, J., Hughes, K.: Reinforcing a philosophy: a counting approach to square functions over local fields. arXiv:2201.09649
2. Bourgain, J., Demeter, C., Guth, L.: Proof of the main conjecture in Vinogradov’s mean value theorem for degrees higher than three. Ann. Math. (2) 184(2):633–682 (2016)
3. Cassels, J.W.S.: Local Fields. London Mathematical Society Student Texts, vol. 3. Cambridge University Press, Cambridge (1986)
4. Chalk, J.H.H.: A $$p$$-adic approach to solutions of a polynomial congruence modulo $$p^\alpha $$. Mathematika 37(2), 209–216 (1990)
5. de Francia, R., José, L.: Estimates for some square functions of Littlewood–Paley type. Publ. Sec. Mat. Univ. Autònoma Barcelona 27(2):81–108 (1983)
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献