Signatures et composantes connexes.
Signatures of fields and extension theory.
Signatures of Higher Level on Rings with Many Units.
Signatures of units and congruences (mod 4) in certain real quadratic fields. II.
Signatures of units and congruences (mod 4) in certain real quadratic fields.
Signatures of units and congruences (mod 4) in certain totally real fields.
Sign-changes of the Thue-Morse Fractal Function and Dirichlet L-Series.
Signed bits and fast exponentiation
An exact analysis is given of the benefits of using the non-adjacent form representation for integers (rather than the binary representation), when computing powers of elements in a group in which inverting is easy. By counting the number of multiplications for a random exponent requiring a given number of bits in its binary representation, we arrive at a precise version of the known asymptotic result that on average one in three signed bits in the non-adjacent form is non-zero. This shows that...
Signed Selmer groups over -adic Lie extensions
Let be an elliptic curve over with good supersingular reduction at a prime and . We generalise the definition of Kobayashi’s plus/minus Selmer groups over to -adic Lie extensions of containing , using the theory of -modules and Berger’s comparison isomorphisms. We show that these Selmer groups can be equally described using Kobayashi’s conditions via the theory of overconvergent power series. Moreover, we show that such an approach gives the usual Selmer groups in the ordinary case....
Signs in weight spectral sequences, monodromy-weight conjectures, log Hodge symmetry and degenerations of surfaces
Similitude des multiples des formes d’Albert en caractéristique 2
Étant donnés un corps commutatif de caractéristique , des formes bilinéaires d’Albert et des -formes quadratiques de Pfister, ou des -formes bilinéaires de Pfister et des formes quadratiques d’Albert (resp. des formes bilinéaires d’Albert et des -formes bilinéaires de Pfister avec la condition que , , soient anisotropes), alors on montre que (resp.) si et seulement si est semblable à . Un exemple montre que la condition de l’anisotropie est nécessaire dans le cas bilinéaire....
Simple groups of square order and interesting sequence of primes
Simple proofs of some generalizations of the Wilson’s theorem
In this paper a remarkable simple proof of the Gauss’s generalization of the Wilson’s theorem is given. The proof is based on properties of a subgroup generated by element of order 2 of a finite abelian group. Some conditions equivalent to the cyclicity of (Φ(n), ·n), where n > 2 is an integer are presented, in particular, a condition for the existence of the unique element of order 2 in such a group.
Simple proofs of the Siegel-Tatuzawa and Brauer-Siegel theorems
We give a simple proof of the Siegel-Tatuzawa theorem according to which the residues at s = 1 of the Dedekind zeta functions of quadratic number fields are effectively not too small, with at most one exceptional quadratic field. We then give a simple proof of the Brauer-Siegel theorem for normal number fields which gives the asymptotics for the logarithm of the product of the class number and the regulator of number fields.
Simple zeros of degree 2 -functions
We prove that the complete -functions of classical holomorphic newforms have infinitely many simple zeros.
Simple zeros of the Ramanujan ...-Dirichlet series.
Simple zeros of the zeta function of a quadratic number field. I.
Simples remarques sur les racines entières des équations cubiques
Simples remarques sur les racines entières des équations cubiques
Simplest Cubic Fields.