Published and Accepted
14) Restricted slowly growing digits for infinite iterated function systems.
Journal of Mathematical Analysis and Applications}. Vol 549(1): (2025). (with G. Gonzalez Robert, M. Hussain and H. Takahasi).
13) Complex numbers with a prescribed order of approximation and Zaremba's conjecture.
Journal of Number Theory. (with G. Gonzalez Robert and M. Hussain).
12) Metrical properties of exponentially growing partial quotients.
Forum Mathematicum. (with M. Hussain).
11) Radical bound for Zaremba's conjecture.
Bull. Lond. Math. Soc., 56: 2615-2624 (2024).
10) Metrical properties of finite product of partial quotients in arithmetic progressions.
Accepted in Annali della Scuola Normale Superiore di Pisa. Preprint: arXiv (with M. Hussain).
9) Hausdorff dimension for sets of continued fractions of formal Laurent series.
Finite Fields and Their Applications , Vol 95 (2024), 102377 (with M. Hussain).
8) Hausdroff dimension for the set with exponentially growing partial quotients in their Lüroth expansion.
Discrete and Continuous Dynamical Systems , Vol 44(6): (2024), 1747-1767 (with M. Hussain and Z. Zhang).
7) Difference of irrationality measure functions.
Monatshefte für Mathematik, Vol 204, 171–189 (2024) (with V. Rudykh).
6) Metrical properties for the product of multiple partial quotients vs single partial quotient in continued fractions.
Discrete and Continuous Dynamical Systems , V. 44, Issue 1: 154-181 (2024) (with B. Li and M. Hussain).
5) A note on badly approximable systems of linear forms over formal series.
Research in Number Theory , 9, 31 (2023) , (with M. Hussain).
4) Rational approximations to two irrational numbers.
Moscow Journal of Combinatorics and Number Theory Vol. 11 (2022), No. 1, 1–10.
3) On the derivative of iterations of the Minkowski question mark function at special points.
Funct. Approx. Comment. Math. 66(2): 191-202, (2022).
2) On Gauss and Kloosterman sums.
Far Eastern Mathematical Journal . (in Russian), V. 20. No 1. (2020), 9–14. (with M. Avdeeva and N. Gorbatuk).
1) Diophantine properties of fixed points of Minkowski question mark function.
Acta Arithmetica. 195 (2020): 367-382. (with D. Gayfulin).
Other writings
Humanity's Last Exam.
Preprint: arXiv (Long Phan et al.)
Dataset contributor for the most modern benchmark for evaluating the capabilities of LLM's.
Submitted and Pre-prints
Approximation by Uniformly distributed sequences
Submitted. (with G. Gonzalez Robert, M. Hussain and B. Ward).
On a conjecture of Cusick on sums of Cantor sets.
Submitted. Preprint: arXiv.
Dirichlet’s improvability in Lp norms.
Submitted. Preprint: arXiv (with N. Moshchevitin).
Metrical properties of the product of partial quotients with geometric mean in continued fractions.
Preprint: arXiv (with B. Li and M. Hussain).
Weighted approximation for limsup sets.
Preprint: arXiv (with G. Gonzalez Robert, M. Hussain and B. Ward).
Last update: 12.06.2025