15 zoekresultaten voor “number theory” in de Publieke website
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Kummer theory for commutative algebraic groups
This dissertation is a collection of four research articles devoted to the study of Kummer theory for commutative algebraic groups.
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Decompositions in algebra
We show that Kirchhoff ’s law of conservation holds for non-commutative graph flows if and only if the graph is planar. We generalize the theory of (Euclidean) lattices to infinite dimension and consider the ring of algebraic integers as such a lattice.
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Enumerative arithmetic
This thesis consists of three chapters. Each chapter is on a different subject. However, all three chapters address issues that arise in counting arithmetically interesting objects.
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Modular curves, Arakelov theory, algorithmic applications
Promotor: S.J. Edixhoven, Co-promotor: R.S. de Jong
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Torsion points on elliptic curves over number fields of small degree
Promotor: S.J. Edixhoven Co-promotor: L. van Geemen, P. Parent
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On the 16-rank of class groups of quadratic number fields
Promotores: P. Stevenhagen, E. Fouvry (Univeriste Paris Saclay)
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Topological aspects of rational points on K3 surfaces
Promotor: P. Stevenhagen, Co-promotor: R.M. van Luijk
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On p-adic decomposable form inequalities
Promotor: Prof.dr. P. Stevenhagen, Jan-Hendrik Evertse, Co-promotor: Pascal Autissier
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Modular forms of weight one over finite fields
Promotor: S.J. Edixhoven
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On continued fraction algorithms
Promotor: Robert Tijdeman, Co-promotor: Cornelis Kraaikamp
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Inverse Jacobian and related topics for certain superelliptic curves
To an algebraic curve C over the complex numbers one can associate a non-negative integer g, the genus, as a measure of its complexity.
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On the amount of sieving in factorization methods
Promotoren: R. Tijdeman, A.K. Lenstra, Co-promotor: H.J.J. te Riele
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Computational aspects of class group actions and applications to post-quantum cryptography
Most of current public-key cryptography is considered insecure against attacks from sufficiently powerful quantum computers. Post-quantum cryptography studies methods to secure information resistant against such attacks. One proposal is isogeny-based cryptography, which bases its security on computational…
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The wild Brauer-Manin obstruction on K3 surfaces
In this thesis, rational points on K3 surfaces are studied. In the first part of Chapter 1 the Brauer group and the the Brauer-Manin obstruction are introduced.
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Complex multiplication of abelian surfaces
Promotor: Peter Stevenhagen