نتایج جستجو برای: zeros of abelian integrals
تعداد نتایج: 21170995 فیلتر نتایج به سال:
We give a simple proof of an isomorphism between the two C[t]-modules: the module of relative cohomologies Λ/dH ∧ Λ and the module ofAbelian integrals corresponding to a Morse-plus polynomial H in two variables.Using this isomorphism, we prove existence and deduce some properties of thecorresponding Picard-Fuchs system. Department of Mathematics, Purdue University, West Lafayett...
Eichler integrals play an integral part in the modular parametrizations of elliptic curves. In her master’s thesis, Kodgis conjectures several dozen zeros of Eichler integrals for elliptic curves with conductor ≤ 179. In this paper we prove a general theorem which confirms many of these conjectured zeros. We also provide two ways to generate infinite families of elliptic curves with certain zer...
We study the problem of placing effective upper bounds for the number of zeros of solutions of Fuchsian systems on the Riemann sphere. The principal result is an explicit (non-uniform) upper bound, polynomially growing on the frontier of the class of Fuchsian systems of a given dimension n having m singular points. As a function of n, m, this bound turns out to be double exponential in the prec...
The arithmetic geometric mean algorithm for calculation of elliptic integrals of the first type was introduced by Gauss. The analog algorithm for Abelian integrals of genus 2 was introduced by Richelot (1837) and Humbert (1901). We present the analogous algorithm for Abelian integrals of genus 3.
We prove that the quotient of abelian integrals associated to an elliptic surface is bounded and strictly increasing by first determining the Picard-Fuchs equation satisfied by the a,belian integrals and the Riccati equation satisfied by the quotient of the abelian integrals.
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