Related papers: Non-Archimedean meromorphic solutions of functiona…
The aim of this paper is to put the fundations of a new theory of functions, called holomorphic Cliffordian, which should play an essential role in the generalization of holomorphic functions to higher dimensions. Let R\_{0,2m+1} be the…
Let $L$ be a line bundle on a proper, geometrically reduced scheme $X$ over a non-trivially valued non-Archimedean field $K$. Roughly speaking, the non-Archimedean volume of a continuous metric on the Berkovich analytification of $L$…
We explicitly write dowm integral formulas for solutions to Knizhnik-Zamolodchikov equations with coefficients in non-bounded -- neither highest nor lowest weight -- $\gtsl_{n+1}$-modules. The formulas are closely related to WZNW model at a…
Nonlocal cosmological models derived from String Field Theory are considered. A new method for constructing rolling tachyon solutions in the FRW metric in two field configuration is proposed and solutions of the Friedman equations with…
Firstly, we provide a different proof of an important lemma in Buzzard and Calegari's work on slopes of overconvergent 2-adic modular forms via nonarchimedean linear Hodge-Newton decomposition. The lemma shows that two equivalent matrices…
We study the meromorphic modular forms defined as sums of -k (k>1) powers of integral quadratic polynomials with negative discriminant. These functions can be viewed as meromorphic analogues of the holomorphic modular forms defined in the…
Consider the nonlinear scalar field equation \begin{equation} \label{a1} -\Delta{u}= f(u)\quad\text{in}~\mathbb{R}^N,\qquad u\in H^1(\mathbb{R}^N), \end{equation} where $N\geq3$ and $f$ satisfies the general Berestycki-Lions conditions. We…
In this chapter, we review the Ra\~{n}ada field line solutions of Maxwell's equations in the vacuum, which describe a topologically non-trivial electromagnetic field, as well as their relation with the knot theory. Also, we present a…
Cohomological equations appear frequently in dynamical systems. One of the most classical examples is the Liv\v{s}ic equation $$ v(x) = \alpha \circ F(x) - \alpha(x).$$ The existence and regularity of its solutions $\alpha$ is well…
In this paper, we survey and study definitions and properties of tropical polynomials, tropical rational functions and in general, tropical meromorphic functions, emphasizing practical techniques that can really carry out computations. For…
The main goal of this project is to prove the equivalency of several characterizations of completeness of Archimedean ordered fields; some of which appear in most modern literature as theorems following from the Dedekind completeness of the…
The notion of a noncommutative quasi-resolution is introduced for a noncommutative noetherian algebra with singularities, even for a non-Cohen-Macaulay algebra. If A is a commutative normal Gorenstein domain, then anoncommutative…
A number of results are proved concerning non-real zeros of derivatives of real and strictly non-real meromorphic functions in the plane
We introduce a geometric realization of noncommutative singularity resolutions. To do this, we first present a new conjectural method of obtaining conventional resolutions using coordinate rings of matrix-valued functions. We verify this…
We construct nonlinear entire solutions in $\mathbb{R}^6$ to equations of minimal surface type that correspond to parametric elliptic functionals.
In this article, we study the properties of a class of functional spaces which arise from the investigation of nonlinear differential equations. We establish some integral inequalities then by applying these inequalities, we prove some…
We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.
We give an alternative and simpler method for getting pointwise estimate of meromorphic solutions of homogeneous linear differential equations with coefficients meromorphic in a finite disk or in the open plane originally obtained by Hayman…
This paper introduces noncommutative analogs of monomial symmetric functions and fundamental noncommutative symmetric functions. The expansion of ribbon Schur functions in both of these basis is nonnegative. With these functions at hand,…
The standard $L$-functions of $\mathrm{GL}_{2n}$ expressed in terms of the Friedberg-Jacquet global zeta integrals have better structure for arithmetic applications, due to the relation of the linear periods with the modular symbols. The…