Mathematics Surrounding Applications of Riemann’s Existence Theorem
نویسنده
چکیده
In these notes we collect in one place the various background material involved in applications of Riemann’s existence theorem to questions about polynomials or curves. This will eventually include material on Riemann surfaces, algebraic topology, Galois theory, group theory, ramification, elliptic curves, rigidity,
منابع مشابه
A GAP Package for Braid Orbit Computation and Applications
Let G be a finite group. By Riemann’s Existence Theorem, braid orbits of generating systems of G with product 1 correspond to irreducible families of covers of the Riemann sphere with monodromy group G. Thus many problems on algebraic curves require the computation of braid orbits. In this paper we describe an implementation of this computation. We discuss several applications, including the cl...
متن کاملExistence of Solutions for some Nonlinear Volterra Integral Equations via Petryshyn's Fixed Point Theorem
In this paper, we study the existence of solutions of some nonlinear Volterra integral equations by using the techniques of measures of noncompactness and the Petryshyn's fixed point theorem in Banach space. We also present some examples of the integral equation to confirm the efficiency of our results.
متن کاملExistence of solutions of infinite systems of integral equations in the Frechet spaces
In this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the Fr´echet spaces. Our aim is to provide a few generalization of Tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of Tych...
متن کاملFixed point theorem for non-self mappings and its applications in the modular space
In this paper, based on [A. Razani, V. Rako$check{c}$evi$acute{c}$ and Z. Goodarzi, Nonself mappings in modular spaces and common fixed point theorems, Cent. Eur. J. Math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping $T$ in the modular space $X_rho$ is presented. Moreover, we study a new version of Krasnoseleskii's fixed point theorem for $S+T$, where $T$ is a cont...
متن کاملWhat Gauss told Riemann about Abel’s Theorem
Historian Otto Neuenschwanden studied Riemann’s library record in Göttingen. He also consulted job position letters in Germany in the 3rd quarter of the 19th century. These show Riemann relied on personal discussions with Gauss (in the late 1840’s) about harmonic functions. Mathematicians rejected that early approach after Riemann’s death (in 1866) until near the end of the 20th century’s 1st q...
متن کامل