Sökning: "Elliptic curves"

Visar resultat 1 - 5 av 8 avhandlingar innehållade orden Elliptic curves.

  1. 1. Counting rational points on genus one curves

    Författare :Manh Hung Tran; Göteborgs universitet; Göteborgs universitet; Gothenburg University; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Diophantine equations; rational points; Elliptic curves; genus; descent; determinant method; cubic and quartic curves; genus;

    Sammanfattning : This thesis contains two papers dealing with counting problems for curves of genus one. We obtain uniform upper bounds for the number of rational points of bounded height on such curves. The main tools to study these problems are descent and various refined versions of Heath-Brown’s p-adic determinant method. LÄS MER

  2. 2. The density of rational points and invariants of genus one curves

    Författare :Manh Hung Tran; Chalmers University of Technology; []
    Nyckelord :genus one; discriminant; modular form; Elliptic curve; height; descent; determinantal representation; invariant; rational point; theta function.; determinant method;

    Sammanfattning : The present thesis contains three papers dealing with two arithmetic problems on curves of genus one, which are closely related to elliptic curves. The first problem is to study the density of rational points presented in Papers I and II. LÄS MER

  3. 3. Point counts and the cohomology of moduli spaces of curves

    Författare :Jonas Bergström; Carel Faber; Lothar Göttsche; KTH; []
    Nyckelord :NATURAL SCIENCES; NATURVETENSKAP; MATHEMATICS; MATEMATIK;

    Sammanfattning : n this thesis we count the number of points defined over finite fields of certain moduli spaces of pointed curves. The aim is primarily to gain cohomological information. Paper I is joint work with Orsola Tommasi. Here we present details of the method of finding cohomological information on moduli spaces of curves by counting points. LÄS MER

  4. 4. Lightweight Cryptographic Group Key Management Protocols for the Internet of Things

    Författare :Teklay Gebremichael; Mikael Gidlund; Ulf Jennehag; Andreas Jacobsson; Mittuniversitetet; []
    Nyckelord :NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; Privacy and security of the IoT; IoT group key management; lightweight key management protocols; elliptic curve cryptography; proximity-based authentication;

    Sammanfattning : The Internet of Things (IoT) is increasingly becoming an integral component of many applications in consumer, industrial and other areas. Notions such as smart industry, smart transport, and smart world are, in large part, enabled by IoT. LÄS MER

  5. 5. Computations in the Grothendieck Group of Stacks

    Författare :Daniel Bergh; Torsten Ekedahl; David Rydh; Jochen Heinloth; Stockholms universitet; []
    Nyckelord :NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; matematik; Mathematics;

    Sammanfattning : Given an algebraic group, one may consider the class of its classifying stackin the Grothendieck group of stacks. This is an invariant studied byEkedahl. For certain connected groups, called the special groups bySerre and Grothendieck, the invariant simply gives the inverse of the class ofthe group itself. LÄS MER