Makoto Kawashima's page

Domain of Reserch

I am currently an associate professor at Meiji Gakuin University and a member of the Institute for Mathematical Informatics at Meiji Gakuin University.

My main research areas are transcendental number theory and Diophantine approximation. In particular, I am interested in the Grothendieck–André period conjecture, such as the irrationality and transcendence of periods of algebraic varieties. These periods are related to the class of power series called G-functions, defined by C. Siegel—for example, solutions of the Gauss–Manin connection of family of algebraic varieties—and are connected to the theory of differential equations and algebraic geometry.

To study the arithmetic properties of periods, I use and develop Padé approximations—a type of rational approximation of power series—originating with Ch. Hermite. So far, my work has focused on investigating the complex and p-adic properties of special values of functions related to hypergeometric functions.

Publications

10. On the linear independence of p-adic polygamma functions, (with A. Poëls), Mathematika, Volume71, Issue4, October 2025.［journal］［arXiv］

9. Rodrigues formula and linear independence for values of hypergeometric functions with parameters vary, Journal of Australian Math. Soc., 117(3), 308-344, (2023).［journal］［arXiv］

8. Padé approximation for a class of hypergeometric functions and parametric geometry of numbers, (with A. Poëls), Journal of Number Theory, 243, 646-687, (2023).［journal］［arXiv］

7. S-unit equation in two variables and Pade approximations, (with N. Hirata-Kohno, A. Poëls and Y. Washio), International Journal of Number Theory, 19(10), 2427-2442, (2023).［journal］［arXiv］

6. The digit exchanges in the beta expansion of algebraic numbers, (with H. Kaneko), Journal of Number Theory, 241, 430-449, (2022).［journal］［arXiv］

5. Linear independence criteria for generalized polylogarithms with distinct shifts, (with Sinnou David, N. Hirata-Kohno), Acta Arithmetica, 206(2),127-169, (2022).［journal］［arXiv］

4. Linear Forms in Polylogarithms, (with S. David, N. Hirata-Kohno), Annali della Scuola Normale Superiore di Pisa, Classe di Scienze XXIII(3), 1447-1490, (2022).［journal］［arXiv］

3. Can polylogarithms at algebraic points be linearly independent? (with S. David and N. Hirata-Kohno), Moscow Journal of Combinatorics and Number Theory, 9(4), 389-406, (2020).［journal］［arXiv］

2. A lower bound of the dimension of the vector space spanned by the special values of certain functions, (with M. Hirose and N. Sato), Tokyo Journal of Mathematics, 40(2), 439-479, (2017).［pdf］

1. Evaluation of the dimension of the Q-vector space spanned by the special values of the Lerch function, Tsukuba Journal of Mathematics, 38(2), 171-188, (2015).［journal］

Pre-Print

1. Linear independence of values of hypergeometric functions and arithmetic Gevrey series, (with S. David and N. Hirata-Kohno), ［arXiv］

2. Hermite's approach to Abelian integrals revisited, ［arXiv］

3. Pad\'{e} approximations for products of functions, ［arXiv］

LINK

Meiji Gakuin Number Theory Seminar

Contact me

Mail: kawasima at mi dot meijigakuin dot ac dot jp

Postal Address

Meiji Gakuin University

1518, Kamikurata, Totsuka, Yokohama, Kanagawa, 244-8539

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