Zobrazeno 1 - 10
of 154
pro vyhledávání: '"12H25"'
Autor:
Ohkubo, Shun
One of the phenomena peculiar in the theory of $p$-adic differential equations is that solutions $f$ of $p$-adic differential equations defined on open discs may satisfy growth conditions at the boundaries. This phenomenon is first studied by Dwork,
Externí odkaz:
http://arxiv.org/abs/2411.16562
Autor:
Houédry, Pierre
In this paper, we introduce novel concepts and establish a formal framework for twisted differential operators in the context of several variables. The focus is on twisted coordinates within Huber rings, which facilitate the construction of diverse r
Externí odkaz:
http://arxiv.org/abs/2309.13277
Autor:
Asakura, Masanori, Hagihara, Kei
Recently, Kedlaya proves certain formula describing explicitly the Frobenius structure on a hypergeometric equation. In this paper, we give a generalization of it. In our case, the Frobenius matrix is no longer described by p-adic gamma function, and
Externí odkaz:
http://arxiv.org/abs/2307.08940
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:
Azzouz, Tinhinane A.
The primary objective of this paper is to generalize the results of [arXiv:2111.03548] to the case of quasi-smooth Berkovich curves by establishing a connection between the spectrum and the radii of convergence. To achieve this, we investigate the co
Externí odkaz:
http://arxiv.org/abs/2303.06014
Autor:
Furusho, Hidekazu
This paper introduces a $p$-adic analogue of Gauss's hypergeometric function which is constructed along ideas different from Dwork's. Our construction is based on a relationship between the hypergeometric function and the KZ equation. We perform a re
Externí odkaz:
http://arxiv.org/abs/2211.07155
Autor:
Pascoe, J. E.
Many theorems in complex analysis propagate analyticity, such as the Forelli theorem, edge-of-the-wedge theorem and so on. We give a germination theorem which allows for general analytic propagation in complete normed fields. In turn, we develop gene
Externí odkaz:
http://arxiv.org/abs/2210.14903
Autor:
Azzouz, Tinhinane A.
This paper extends our previous works arXiv:1802.07306 [math.NT], arXiv:1808.02382 [math.NT] on determining the spectrum, in the Berkovich sense, of ultrametric linear differential equations. Our previous works focused on equations with constant coef
Externí odkaz:
http://arxiv.org/abs/2111.03548
Autor:
Berger, Laurent
We ask several questions about substitution maps in the Robba ring. These questions are motivated by $p$-adic Hodge theory and the theory of $p$-adic dynamical systems. We provide answers to those questions in special cases, thereby generalizing resu
Externí odkaz:
http://arxiv.org/abs/2012.01904
Autor:
Bojković, Velibor
Let $(k,|\cdot|)$ be a complete and algebraically closed valued field extension of $(\mathbb{Q}_p,|\cdot|_p)$. Given a finite morphism $\varphi:\mathscr{D}_1\to \mathscr{D}_2$ of unit discs over $k$, a differential module $(M,D)$ on $\mathscr{D}_1$ a
Externí odkaz:
http://arxiv.org/abs/2009.10485