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Class invariants and cyclotomic unit groups from special values of modular units

Amanda Folsom (2008)

Journal de Théorie des Nombres de Bordeaux

In this article we obtain class invariants and cyclotomic unit groups by considering specializations of modular units. We construct these modular units from functional solutions to higher order $q$ -recurrence equations given by Selberg in his work generalizing the Rogers-Ramanujan identities. As a corollary, we provide a new proof of a result of Zagier and Gupta, originally considered by Gauss, regarding the Gauss periods. These results comprise part of the author’s 2006 Ph.D. thesis [6] in which...

Class Invariants for Quartic CM Fields

Eyal Z. Goren, Kristin E. Lauter (2007)

Annales de l’institut Fourier

One can define class invariants for a quartic primitive CM field $K$ as special values of certain Siegel (or Hilbert) modular functions at CM points corresponding to $K$ . Such constructions were given by de Shalit-Goren and Lauter. We provide explicit bounds on the primes appearing in the denominators of these algebraic numbers. This allows us, in particular, to construct $S$ -units in certain abelian extensions of a reflex field of $K$ , where $S$ is effectively determined by $K$ , and to bound the primes appearing...

Class numbers of ring class fields of prime conductor

Omer Kucuksakalli (2012)

Acta Arithmetica

Construction of Ray class fields by elliptic units

Reinhard Schertz (1997)

Journal de théorie des nombres de Bordeaux

From complex multiplication we know that elliptic units are contained in certain ray class fields over a quadratic imaginary number field $K$ , and Ramachandra [3] has shown that these ray class fields can even be generated by elliptic units. However the generators constructed by Ramachandra involve very complicated products of high powers of singular values of the Klein form defined below and singular values of the discriminant $Δ$ . It is the aim of this paper to show, that in many cases a generator...

Cuspidal groups, ordinary Eisenstein series, and Kubota-Leopoldt p-adic L-functions

Marc Nirenberg (2001)