Essays about: "talteori"
Showing result 1 - 5 of 7 essays containing the word talteori.
-
1. Scheme Theory & Weak Mordell-Weil for Elliptic Curves Over Number Fields
University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)Abstract : We provide an introduction to scheme-theoretic algebraic geometry, which studies spaces that are in essence locally solutions to systems of polynomial equations, and prove the weak Mordell-Weil theorem. The weak Mordell-Weil theorem states that for an elliptic curve $E$ over a number field $K$, the quotient $E(K)/mE(K)$ is finite for all $m\geq 2$. READ MORE
-
2. From Multilinear Kakeya to Additive Energies : Decoupling and Its Use in Combinatorial Number Theory
University essay from Umeå universitet/Institutionen för matematik och matematisk statistikAbstract : This is a survey of decoupling results in harmonic analysis and their use in combinatorial number theory. The main results are an expository proof of a decoupling inequality for exponential sums in and a new lower bound on the cardinality of the sumsets of certain convex sequences. READ MORE
-
3. On Intersections of Algebraic Curves and Applications to Elliptic Curves
University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten)Abstract : In this thesis we state and give elementary proofs for some fundamental results about intersections of algebraic curves, namely Bezout's, Max Noether's, Pappus's, Pascal's and Chasles' theorems. Our main tools are linear algebra and basic ring theory. We conclude the thesis by applying the results to elliptic curves.. READ MORE
-
4. On the Asymptotic Behaviour of Sums of Two Squares : Theoretical and Numerical Studies of the Counting Function B(x)
University essay from KTH/Skolan för teknikvetenskap (SCI)Abstract : Studying the distributions of special numbers is a fundamental area of research in number theory. This paper studies the distribution of sums of two squares using analytic number theory. The asymptotic behaviour of the corresponding counting function, B(x), is the object of study. READ MORE
-
5. Observations on continued fractions from Ford's point of view
University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten)Abstract : Detta är ett projekt på en geometrisk metod för att visualisera beräkning av kedjebråk, som har utvecklats av Lester R. Ford på 1930-talet. Beskrivningen av metoden följs med användning tekniken av Ford cirklar på tre olika fall. READ MORE