Mahler measure of the Horie unit and Weber's class number problem in the cyclotomic ℤ₃-extension of ℚ
Majoration au point 1 des fonctions L associées aux caractères de Dirichlet primitifs, ou au caractère d'une extension quadratique d'un corps quadratique imaginaire principal.
Making sense of capitulation: reciprocal primes
Let ℓ be a rational prime, K be a number field that contains a primitive ℓth root of unity, L an abelian extension of K whose degree over K, [L:K], is divisible by ℓ, a prime ideal of K whose ideal class has order ℓ in the ideal class group of K, and any generator of the principal ideal . We will call a prime ideal of K ’reciprocal to ’ if its Frobenius element generates for every choice of . We then show that becomes principal in L if and only if every reciprocal prime is not a norm inside...
Maximal unramified extensions of imaginary quadratic number fields of small conductors
We determine the structures of the Galois groups Gal of the maximal unramified extensions of imaginary quadratic number fields of conductors under the Generalized Riemann Hypothesis). For all such , is , the Hilbert class field of , the second Hilbert class field of , or the third Hilbert class field of . The use of Odlyzko’s discriminant bounds and information on the structure of class groups obtained by using the action of Galois groups on class groups is essential. We also use class...
Minoration au point 1 des fonctions L et détermination des corps sextiques abéliens totalement imaginaires principaux
Minorations de discriminants
Modular curves and 11-rank of quadratic fields. (Courbes modulaires et 11-rang de corps quadratiques.)
Modular forms and class number congruences
Mollin's conjecture
Momente der Klassenzahlen binärer quadratischer Formen mit ganzalgebraischen Koeffizienten