Simplicity of twists of abelian varieties
We give some easy necessary and sufficient criteria for twists of abelian varieties by Artin representations to be simple.
Simplification pour les ordres des corps de quaternions totalement définis.
Simultaneous approximation in number fields.
Single polynomials that correspond to pairs of cyclotomic polynomials with interlacing zeros
We give a complete classification of all pairs of cyclotomic polynomials whose zeros interlace on the unit circle, making explicit a result essentially contained in work of Beukers and Heckman. We show that each such pair corresponds to a single polynomial from a certain special class of integer polynomials, the 2-reciprocal discbionic polynomials. We also show that each such pair also corresponds (in four different ways) to a single Pisot polynomial from a certain restricted class, the cyclogenic...
Singular Moduli, Modular Polynomials, and the Index of the Closure of Z [j (...)] in Q (j(...)).
Small discriminants of complex multiplication fields of elliptic curves over finite fields
We obtain a conditional, under the Generalized Riemann Hypothesis, lower bound on the number of distinct elliptic curves over a prime finite field of elements, such that the discriminant of the quadratic number field containing the endomorphism ring of over is small. For almost all primes we also obtain a similar unconditional bound. These lower bounds complement an upper bound of F. Luca and I. E. Shparlinski (2007).
Small generators of function fields
Let be a finite extension of a global field. Such an extension can be generated over by a single element. The aim of this article is to prove the existence of a ”small” generator in the function field case. This answers the function field version of a question of Ruppert on small generators of number fields.
Small limit points of Mahler's measure.
Small points on a multiplicative group and class number problem
Let be an algebraic subvariety of a torus and denote by the complement in of the Zariski closure of the set of torsion points of . By a theorem of Zhang, is discrete for the metric induced by the normalized height . We describe some quantitative versions of this result, close to the conjectural bounds, and we discuss some applications to study of the class group of some number fields.
Small values of zeta-functions of quadratic fields.
Small zeros of hermitian forms over a quaternion algebra
Sobre el índice de irregularidad de los números primos.
Solomon's Zeta Functions over Algebraic Function Fields.
Solution des problèmes de Favard
Solution des problèmes de Favard
Pour tout , on calcule un rang tel que tout entier algébrique de degré au moins ait deux conjugués vérifiant . De plus, on donne une nouvelle preuve de l’égalité .
Solution du problème du dixième discriminant
Solution of a cyclotomic diophantine equation.
Solution of a generalised version of a problem of Rankin on sums of powers of cusp-form coefficients
Solution of small class number problems for cyclotomic fields
Solution of the Classs Number Two Problem for Cyclotomic Fields.