Yu-Chen Sun
References
Balog, A. and Friedlander, J. (1992) ‘A hybrid of theorems of Vinogradov and Piatetski-Shapiro’, Pacific Journal of Mathematics, 156(1), pp. 45–62. doi: 10.2140/pjm.1992.156.45.
Buczolich, Z. (2007) ‘Universally 𝐿1 good sequences with gaps tending to infinity’, Acta Mathematica Hungarica, 117(1-2), pp. 91–114. Available at: https://arxiv.org/pdf/math.DS/0601329.
Green, B. (2005) ‘Roth’s theorem in the primes’, Annals of Mathematics, 161(3), pp. 1609–1636. doi: 10.4007/annals.2005.161.1609.
Krause, B. and Sun, Y. (2025) ‘Quantitative convergence for sparse ergodic averages in 𝐿1’, arXiv preprint, arXiv: 2504.12510.
Li, H. and Pan, H. (2019) ‘The Green-Tao Theorem for Piatetski-Shapiro primes’, arXiv preprint, arXiv: 1901.09372.
Mirek, M. (2015a) ‘Roth’s theorem in the Piatetski-Shapiro primes’, Revista Matemática Iberoamericana, 31(3), pp. 617–656. doi: 10.4171/RMI/848.
Mirek, M. (2015b) ‘Weak type (1,1) inequalities for discrete rough maximal functions’, Journal of Analysis and Mathematics, 127, pp. 303–337.
Piatetski-Shapiro, I.I. (1953) ‘On the distribution of prime numbers in sequences of the form [𝑓(𝑛)]’, Matematicheskii Sbornik, 33(2), pp. 559–566.
Rivat, J. and Sargos, P. (2001) ‘Nombres premiers de la forme ⌊𝑛𝑐⌋’, Canadian Journal of Mathematics, 53(2), pp. 414–433. doi: 10.4153/CJM-2001-017-0.
Rivat, J. and Wu, J. (2001) ‘Prime numbers of the form[nc]’, Glasow Mathematical Journal, 43(2), pp. 237–254. doi: 10.1017/S0017089501020080.
Rosenblatt, J. and Wierdl, M. (1995) ‘Pointwise ergodic theorems via harmonic analysis’, in Petersen, K.E. and Salama, I. (eds.) Ergodic Theory and Harmonic Analysis: Proceedings of the Alexandria Conference 1993. Cambridge: Cambridge University Press, pp. 3–152.
Sun, Y. Du, S. and Pan, H. (2019) ‘Vinogradov three prime theorem with Piatetski-Shapiro primes’, arXiv preprint arXiv: 1912.12572.
Urban, R. and Zienkiewicz, J. (2007). ‘Weak type (1,1) estimates for a class of discrete rough maximal functions’, Mathematical Research Letters, 14(2), pp. 227–237. doi: 10.4310/MRL.2007.v14.n2.a6.
Project summary
In this project we investigate dynamical and form {⌊𝑛𝑐⌋}, for 1<c<2 as large as possible, arithmetic statistics of sequences of the as well as the statistics of the intersection of these sequences with the primes.
Project lead
Yu-Chen Sun is an ERC-sponsored postdoctoral fellow, working under the supervision of Professor Ben Krause (Bristol University). He completed his PhD in 2024 under the advisement of Kaisa Matomaki (University of Turku).
Project contact
Dr Yu-Chen Sun
Senior Research Associate
University of Bristol
Email: gc25763@bristol.ac.uk
Funding disclaimer
This project has been funded by UK Research and Innovation (UKRI) under the European Union’s Horizon Europe Guarantee programme – grant agreement number EP/Y007336/1.
Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or UKRI. Neither the European Union nor the granting authority can be held responsible for them.