Several-variable -adic families of Siegel-Hilbert cusp eigensystems and their Galois representations
Shimura Varieties and Twisted Orbital Integrals.
Shimuras Reziprozitätsgesetz für den Körper der arithmetischen elliptischen Funktionen beliebiger Stufe.
Shtukas and Jacobi sums.
Siegel Modular Forms of Degree Two: Hecke Eigenforms.
Sieve methods and class-number probelms. II.
Sieve methods and class-number problems. I.
Sieve methods and class-number problems III.
Sign functions of imaginary quadratic fields and applications
We propose a definition of sign of imaginary quadratic fields. We give an example of such functions, and use it to define new invariants that are roots of the classical Ramachandra invariants. Also we introduce signed ordinary distributions and compute their signed cohomology by using Anderson's theory of double complex.
Signature defects of Hilbert-Picard modular cusps.
Signature des unités cyclotomiques et parité du nombre de classes des extensions cycliques de de degré premier impair
Signature des unités cyclotomiques et parité du nombre de classes des extensions cycliques de de degré premier impair
Si est une extension abélienne de de degré impair, l’étude du 2-groupe des classes (au sens ordinaire) de (et même celle de la parité du nombre de classes de ) est non triviale, et les algorithmes connus ne dépassent guère le cas .L’expression analytique de s’interprète à l’aide d’indices convenables de groupes d’unités cyclotomiques (Hasse et Leopoldt) ; ce dernier point de vue permet une caractérisation de la parité de , en fonction de l’existence d’unités cyclotomiques totalement...
Signatures of fields and extension theory.
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.
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....
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 the zeta function of a quadratic number field. I.
Simplest Cubic Fields.