All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 121 Next

Displaying 2401 – 2420 of 16555

Showing per page

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 by Shimura's reciprocity law

Alice Gee (1999)

Journal de théorie des nombres de Bordeaux

We apply the Shimura reciprocity law to determine when values of modular functions of higher level can be used to generate the Hilbert class field of an imaginary quadratic field. In addition, we show how to find the corresponding polynomial in these cases. This yields a proof for conjectural formulas of Morain and Zagier concerning such polynomials.

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 Number Two for Real Quadratic Fields of Richaud-Degert Type

Mollin, R. A. (2009)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.This paper contains proofs of conjectures made in [16] on class number 2 and what this author has dubbed the Euler-Rabinowitsch polynomial for real quadratic fields. As well, we complete the list of Richaud-Degert types given in [16] and show how the behaviour of the Euler-Rabinowitsch polynomials and certain continued fraction expansions come into play in the complete determination...

Currently displaying 2401 – 2420 of 16555