Frobenius method for Mahler equations

Autor: Julien ROQUES

Publikováno v: Journal of the Mathematical Society of Japan.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::e93fbb099f320f1d57a199e6b3873411
https://doi.org/10.2969/jmsj/89258925

On the Kernel Curves Associated with Walks in the Quarter Plane

Autor: Thomas Dreyfus, Charlotte Hardouin, Julien Roques, Michael F. Singer

Publikováno v: Transcendence in Algebra, Combinatorics, Geometry and Number Theory. TRANS19 – Transient Transcendence in Transylvania, Brașov, Romania, May 13–17, 2019, Revised and Extended Contributions
Alin Bostan; Kilian Raschel. Transcendence in Algebra, Combinatorics, Geometry and Number Theory. TRANS19 – Transient Transcendence in Transylvania, Brașov, Romania, May 13–17, 2019, Revised and Extended Contributions, 373, Springer International Publishing, pp.61-89, 2021, Springer Proceedings in Mathematics & Statistics, 978-3-030-84303-8. ⟨10.1007/978-3-030-84304-5_3⟩
Transcendence in Algebra, Combinatorics, Geometry and Number Theory ISBN: 9783030843038

International audience; The kernel method is an essential tool for the study of generating series of walks in the quarter plane. This method involves equating to zero a certain polynomial-the kernel polynomial-and using properties of the curve-the ke

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2e20ef2771e8f6e5cf97be522e1b7193
https://hal.science/hal-03513338/file/kernel.pdf

On the Local Structure of Mahler Systems

Autor: Julien Roques

Publikováno v: International Mathematics Research Notices. 2021:9937-9957

This paper is a 1st step in the direction of a better understanding of the structure of the so-called Mahler systems: we classify these systems over the field $\mathscr{H}$ of Hahn series over $\overline{{\mathbb{Q}}}$ and with value group ${\mathbb{

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::d5c03e8ecb7440062bb8df26c8d60310
https://doi.org/10.1093/imrn/rnz349

Functional relations of solutions of $q$-difference equations

Autor: Thomas Dreyfus, Charlotte Hardouin, Julien Roques

Publikováno v: Mathematische Zeitschrift
Mathematische Zeitschrift, 2021, ⟨10.1007/s00209-020-02669-4⟩
Mathematische Zeitschrift, Springer, 2021, ⟨10.1007/s00209-020-02669-4⟩

In this paper, we study the algebraic relations satisfied by the solutions of q-difference equations and their transforms with respect to an auxiliary operator. Our main tools are the parametrized Galois theories developed in Hardouin and Singer (Mat

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::46e01b03d066381d832632b2bd74c134
https://hal.science/hal-01959032

On some arithmetic properties of Mahler functions

Autor: Sara Checcoli, Julien Roques

Publikováno v: Israël Journal of Mathematics
Israël Journal of Mathematics, The Hebrew University Magnes Press, 2018, 228 (2), pp.801-833
Israël Journal of Mathematics, Hebrew University Magnes Press, 2018, 228 (2), pp.801-833

Mahler functions are power series f(x) with complex coefficients for which there exist a natural number n and an integer l ≥ 2 such that f(x), f(xl),..., $$f({x^{{\ell ^{n - 1}}}}),f({x^{{\ell ^n}}})$$ are linearly dependent over ℂ(x). The study

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c64b0fddae7ec6ab0f0b40c218e75dd6
https://hal.archives-ouvertes.fr/hal-01983025