Comparing orders of Selmer groups
Using both class field and Kummer theories, we propose calculations of orders of two Selmer groups, and compare them: the quotient of the orders only depends on local criteria.
Compatibilité de la suite exacte de Poitou-Tate aux mesures de Haar
Compatibility of the theta correspondence with the Whittaker functors
We prove that the global geometric theta-lifting functor for the dual pair is compatible with the Whittaker functors, where is one of the pairs , or . That is, the composition of the theta-lifting functor from to with the Whittaker functor for is isomorphic to the Whittaker functor for .
Complete residue systems in the quadratic domain .
Completely normal elements in some finite abelian extensions
We present some completely normal elements in the maximal real subfields of cyclotomic fields over the field of rational numbers, relying on the criterion for normal element developed in [Jung H.Y., Koo J.K., Shin D.H., Normal bases of ray class fields over imaginary quadratic fields, Math. Z., 2012, 271(1–2), 109–116]. And, we further find completely normal elements in certain abelian extensions of modular function fields in terms of Siegel functions.
Completeness of the absolute Galois group of the rational number field.
Comportement des fonctions -adiques au voisinage de zéro
Composite rational functions expressible with few terms
We consider a rational function which is ‘lacunary’ in the sense that it can be expressed as the ratio of two polynomials (not necessarily coprime) having each at most a given number of terms. Then we look at the possible decompositions , where are rational functions of degree larger than 1. We prove that, apart from certain exceptional cases which we completely describe, the degree of is bounded only in terms of (and we provide explicit bounds). This supports and quantifies the intuitive...
Composition of norm-type forms.
Comptage exact de discriminants d'extensions abéliennes
Le but de cet article est d’expliquer comment calculer exactement le nombre de classes d’isomorphismes d’extensions abéliennes de en degré inférieur ou égal à et de discriminant majoré par une borne donnée. On parvient par exemple à calculer le nombre de corps cubiques cycliques de discriminant inférieur ou égal à .
Computation of 2-groups of positive classes of exceptional number fields
We present an algorithm for computing the 2-group of the positive divisor classes in case the number field has exceptional dyadic places. As an application, we compute the 2-rank of the wild kernel in .
Computation of Hilbert sequence for composite quadratic extensions using different type of primes in .
Computation of L-series for elliptic curves over function fields.
Computation of relative class numbers of imaginary abelian number fields.
Computation of relative integral bases for algebraic number fields.
Computation of the fundamental units and the regulator of a cyclic cubic function field.
Computational proof of some theorems on class numbers
Computations of cyclotomic lattices.
Computations of Iwasawa invariants and
Computations of Witt Groups of Finite Groups.