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pro vyhledávání: '"Roques, Julien"'
The differential nature of solutions of linear difference equations over the projective line was recently elucidated. In contrast, little is known about the differential nature of solutions of linear difference equations over elliptic curves. In the
Externí odkaz:
http://arxiv.org/abs/2409.10092
Given a linear differential equation with coefficients in $\mathbb{Q}(x)$, an important question is to know whether its full space of solutions consists of algebraic functions, or at least if one of its specific solutions is algebraic. After presenti
Externí odkaz:
http://arxiv.org/abs/2304.05061
Autor:
Roques, Julien, Singer, Michael F.
We study the form of possible algebraic relations between functions satisfying linear differential equations. In particular , if f and g satisfy linear differential equations and are algebraically dependent, we give conditions on the differential Gal
Externí odkaz:
http://arxiv.org/abs/2011.01717
Publikováno v:
Springer Proceedings in Mathematics and Statistics. Vol. 373, (2021), p.61-89
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 kernel curve, this defi
Externí odkaz:
http://arxiv.org/abs/2004.01035
Akademický článek
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Publikováno v:
Journal de l'\'Ecole polytechnique - Math\'ematiques. (2021), vol. 8, p. 147-168
We develop general criteria that ensure that any non-zero solution of a given second-order difference equation is differentially transcendental, which apply uniformly in particular cases of interest, such as shift difference equations, q-dilation dif
Externí odkaz:
http://arxiv.org/abs/1809.05416
Publikováno v:
Journal of Combinatorial Theory, Series A, (2020), vol. 174, p. 105251
We use Galois theory of difference equations to study the nature of the generating series of (weighted) walks in the quarter plane with genus zero kernel curve. Using this approach, we prove that the generating series do not satisfy any nontrivial (p
Externí odkaz:
http://arxiv.org/abs/1710.02848
Publikováno v:
Inventiones Mathematicae, 213 (2018), no.1, 139-203
In the present paper, we introduce a new approach, relying on the Galois theory of difference equations, to study the nature of the generating series of walks in the quarter plane. Using this approach, we are not only able to recover many of the rece
Externí odkaz:
http://arxiv.org/abs/1702.04696
Publikováno v:
Mathematische Zeitschrift. Vol. 298, (2021), no. 3, p. 1751-1791
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 tool is the parametrized Galois theories developed in two papers. The first pa
Externí odkaz:
http://arxiv.org/abs/1603.06771
Publikováno v:
Journal of the European Mathematical Society (JEMS), 20 (2018), no.9, 2209-2238
The last years have seen a growing interest from mathematicians in Mahler functions. This class of functions includes the generating series of the automatic sequences. The present paper is concerned with the following problem, which is omnipresent in
Externí odkaz:
http://arxiv.org/abs/1507.03361