A probabilistic and deterministic modular algorithm for computing Groebner basis over $\Q$.

translate for the first time the Frobenius problem into an algebraic setting, showing that the Frobenius number is the degree of the Hilbert-Poincar´e series written as a

restrictive conditions is Lemma 2.1 and Theorem 3.1. The problems of perfection are avoided in these results by restricting the morphisms in the category with char p. These problems

Nevertheless, there is a result that partially answers the question, namely Diamond proved (see Thm. 2, [11]) that if the level raising condition holds modulo some power of p, then

We show here that in order to strip powers of p from the level of a Galois representation which is strongly modular, it is necessary in general to consider the Galois

It allows one to see such a Galois representation that is modular of level N, weight 2 and trivial Nebentypus as one that is modular of level N p, for a prime p coprime to N , when

We show here that in order to strip powers of p from the level of a Galois representation which is strongly modular, it is necessary in general to consider the Galois

Crucial ingredients are the fact that a Cauchy–Lipschitz theorem for differential systems holds over divided power rings (Proposition 3.4) and the fact that Newton iteration can be

Basis algorithms related to HNF or SNF. Storjohann’s HNF algorithm [Sto00, Chap. Some of them can be adapted as basis algorithms. The asymptotically fastest basis algorithm among