New formulas for the class number of imaginary quadratic fields
New formulations of the class number one problem
Nombre de classes d'idéaux d'une extension diédrale de degré 8 de Q.
Nombre de classes, unités et bases d’entiers des extensions cubiques cycliques de
Nombres de Hurwitz et régularité des idéaux premiers
Nombres de Hurwitz et unités elliptiques. Un critère de régularité pour les extensions abéliennes d'un corps quadratique imaginaire
Non-abelian congruences between -values of elliptic curves
Let be a semistable elliptic curve over . We prove weak forms of Kato’s -congruences for the special values More precisely, we show that they are true modulo , rather than modulo . Whilst not quite enough to establish that there is a non-abelian -function living in , they do provide strong evidence towards the existence of such an analytic object. For example, if these verify the numerical congruences found by Tim and Vladimir Dokchitser.
Non-abelian -adic -functions and Eisenstein series of unitary groups – The CM method
In this work we prove various cases of the so-called “torsion congruences” between abelian -adic -functions that are related to automorphic representations of definite unitary groups. These congruences play a central role in the non-commutative Iwasawa theory as it became clear in the works of Kakde, Ritter and Weiss on the non-abelian Main Conjecture for the Tate motive. We tackle these congruences for a general definite unitary group of variables and we obtain more explicit results in the...
Noncyclotomic -extensions of imaginary quadratic fields.
Nonvanishing of a certain Bernoulli number and a related topic
Let be an odd prime number with q an odd integer. Let δ (resp. φ) be an odd (resp. even) Dirichlet character of conductor p and order (resp. order dividing q), and let ψₙ be an even character of conductor and order pⁿ. We put χ = δφψₙ, whose value is contained in . It is well known that the Bernoulli number is not zero, which is shown in an analytic way. In the extreme cases and q, we show, in an algebraic and elementary manner, a stronger nonvanishing result: for any pⁿth root ξ...
Nonvanishing of L-functions for GL(2).
Norm distribution in Galois orbits.
Normal basis and Greenberg' s conjecture.
Norms from Quadratic Fields and Their Relation to Noncommuting 2 x 2 Matrices III. A Link between the 4-rank of the Ideal Class Groups in...(..m) and in ...(...-m).
Note on an index formula of elliptic units in a ring class field II
Note on class groups of algebraic function fields.
Note on the class-number of the maximal real subfield of a cyclomatic field.
Notes on small class numbers
Notions relatives de régulateurs et de hauteurs