Publications

[Peer-reviewed papers]

1. A criterion for the simple normality of fractional powers of two via the Riemann zeta function, Canad. J. Math. 2025, 1–24 (with Yuya Kanado) [journal] [arXiv]

2. Mills' constant is irrational, Mathematika, 71 (2025), No.3, e70027 [journal] [arXiv] 

3. Some remarks on the $[x/n]$-sequence, Res. number theory, 11 (2025) (with  Yuta Suzuki, Wataru Takeda, Yuuya Yoshida) [journal] [arXiv]

4. Palindromes and Antipalindromes in Short Intervals,  J. Integer Seq. 26 (2023),  Article 23.9.5, 28 pp. (with Prapanpong Pongsriiam). [journal]

5. A system of certain linear Diophantine equations on analogs of squares, Acta Arith. 207 (2023), 251-277, (with Yuya Kanado). [journal][arXiv]

6. Transcendence of values of the iterated exponential function at algebraic points, J. Integer Seq. 26 (2023), Art. 23.3.3, 18 pp. (with Hirotaka Kobayashi, Wataru Takeda). [journal][arXiv] 

7. Topological properties and algebraic independence of sets of prime-representing constants. Mathematika, 68 (2022), no. 2, 429–453 (with Wataru Takeda). [journal] [arXiv]

8. Linear equations with two variables in Piatetski-Shapiro sequences, Acta Arith. 202 (2022), no. 2, 161–171. [journal] [arXiv]

9. Construction of a one-dimensional set which asymptotically and omnidirectionally contains arithmetic progressions. J. Fractal Geom. 7 (2020), no. 4, 319–327. [journal] [arXiv]

10. Prime-representing functions and Hausdorff dimension. Acta Math. Hungar. 165 (2021), no. 1, 203–217. [journal] [arXiv] 

11. Linear Diophantine equations in Piatetski-Shapiro sequences, Acta Arith. 200 (2021), no. 1, 91–110 (with Toshiki Matsusaka).  [journal] [arXiv] 

12. Distributions of finite sequences represented by polynomials in Piatetski-Shapiro sequences, J. Number Theory, Volume 222, 2021, 115–156 (with Yuuya Yoshida). [journal] [arXiv] 

13. A fractal proof of the infinitude of primes. Lith.Math.J. 59 (2019), no. 3, 408–411. [journal] [arXiv] 

14. Dimensions of sets which uniformly avoid arithmetic progressions, Int. Math. Res. Not. IMRN 2019, no. 14, 4419–4430 (with Jonathan M. Fraser and Han Yu).  [journal] [arXiv] 

15. Arithmetic progressions in the graphs of slightly curved sequences, J. Integer Seq. 22 (2019), no. 2, Art. 19.2.1, 25 pp (with Yuuya Yoshida).  [journal] [arXiv] 

[Proceedings (not peer-reviewed]

1. Three-term arithmetic progressions of Piatetski-Shapiro sequences, RIMS 講究録, No.2196 Analytic Number Theory and Related Topics 解析的整数論とその周辺.  [link]

2. Szemeredi’s theorem and fractal dimensions of sets avoiding (k,ε)-arithmetic progressions, RIMS 講究録, No.2176, Research on the Theory of Random Dynamical Systems and Fractal Geometry ランダム力学系とフラ クタル幾何学の研究. [link]

3. 弱い等差数列とフラクタル次元を用いた Szemerediの定理と同値な条件について, RIMS 講究録 No.2162 Analytic Number Theory and Related Topics 解析的整数論とその周辺. [link]

4. On a simple proof of slightly curved sequences containing arbitrarily long arithmetic progressions, RIMS 講究録, No.2131 Analytic Number Theory and Related Topics 解析的整数論とその周辺. [link]

[Preprints]

1. Transcendency of variants of Mills' constant, preprint 2025 [arXiv]. 

2. Intervals without primes near an iterated linear recurrence sequence, preprint 2025 [arXiv]

3.  Normality of algebraic numbers and the Riemann zeta function, preprint 2024 (with Yuya Kanado) [arXiv] 

4.  Finiteness of solutions to linear Diophantine equations on Piatetski-Shapiro sequences, preprint 2023. [arXiv]

5.  New bounds for dimensions of a set uniformly avoiding multi-dimensional arithmetic progressions, preprint 2019. [arXiv]

6.  New fractal dimensions and some applications to arithmetic patches, preprint 2018. [arXiv]

Latest update: May. 8, 2025