Extensions diedrales et courbes elliptiques
Extensions galoisiennes d'un corps local à groupes d'inertie cycliques.
Extensions icosaédriques
Extensions infinies identiquement ramifiées.
Extensions non abéliennes de degré d’un corps de nombres : étude locale-globale
Extensions of asymptotic expansions from Chapter 15 of Ramanujan's second notebook.
Extensions of Bauer's identical congruences
Extensions of Büchi's problem: Questions of decidability for addition and kth powers
We generalize a question of Büchi: Let R be an integral domain, C a subring and k ≥ 2 an integer. Is there an algorithm to decide the solvability in R of any given system of polynomial equations, each of which is linear in the kth powers of the unknowns, with coefficients in C? We state a number-theoretical problem, depending on k, a positive answer to which would imply a negative answer to the question for R = C = ℤ. We reduce a negative answer for k = 2 and for...
Extensions of classical congruences for parameters in binary quadratic forms
Extensions of finite group schemes, and Hopf Galois theory over a complete discrete valuation ring.
Extensions of some formulae of A. Selberg.
Extensions of some parametric families of -triples.
Extensions of the Bloch–Pólya theorem on the number of real zeros of polynomials
We prove that there are absolute constants and such that for everythere aresuch thathas at least distinct sign changes in . This improves and extends earlier results of Bloch and Pólya.
Extensions of the Cugiani-Mahler theorem
In 1955, Roth established that if is an irrational number such that there are a positive real number and infinitely many rational numbers with and , then is transcendental. A few years later, Cugiani obtained the same conclusion with replaced by a function that decreases very slowly to zero, provided that the sequence of rational solutions to is sufficiently dense, in a suitable sense. We give an alternative, and much simpler, proof of Cugiani’s Theorem and extend it to simultaneous...
Extensions of the Gauss-Wilson theorem.
Extensions of Three Theorems of Nagell
Three theorems of Nagell of 1923 concerning integer values of certain sums of fractions are extended.
Extensions quadratiques 2-birationnelles de corps totalement réels.
We characterize 2-birational CM-extensions of totally real number fields in terms of tame ramification. This result completes in this case a previous work on pro-l-extensions over 2-rational number fields.
Extensions quaternioniennes d’un corps de caractéristique différente de
Extensions quaternioniennes d'un corps de nombres
Extensions with restricted ramification and duality for arithmetic schemes