The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “A determinant formula for the relative class number of an imaginary abelian number field”

Bernoulli numbers, Hurwitz numbers, p-adic L-functions and Kummer's criterion.

Alvaro Lozano Robledo (2007)

RACSAM

Similarity:

Let K = Q(ζ) and let h be its class number. Kummer showed that p divides h if and only if p divides the numerator of some Bernoulli number. In this expository note we discuss the generalizations of this type of criterion to totally real fields and quadratic imaginary fields.

A generalization of Scholz’s reciprocity law

Mark Budden, Jeremiah Eisenmenger, Jonathan Kish (2007)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We provide a generalization of Scholz’s reciprocity law using the subfields K 2 t - 1 and K 2 t of ℚ ( ζ p ) , of degrees 2 t - 1 and 2 t over ℚ , respectively. The proof requires a particular choice of primitive element for K 2 t over K 2 t - 1 and is based upon the splitting of the cyclotomic polynomial Φ p ( x ) over the subfields.

Non-abelian congruences between L -values of elliptic curves

Daniel Delbourgo, Tom Ward (2008)

Annales de l’institut Fourier

Similarity:

Let E be a semistable elliptic curve over ℚ . We prove weak forms of Kato’s K 1 -congruences for the special values L 1 , E / ℚ ( μ p n , Δ p n ) . More precisely, we show that they are true modulo p n + 1 , rather than modulo p 2 n . Whilst not quite enough to establish that there is a non-abelian L -function living in K 1 ℤ p [ [ Gal ( ℚ ( μ p ∞ , Δ p ∞ ) / ℚ ) ] ] , they do provide strong evidence towards the existence of such an analytic object. For example, if n = 1 these verify the numerical congruences found by Tim and Vladimir Dokchitser.