Class number calculation using Siegel functions

On the Siegel–tatuzawa Theorem for a Class of L-functions

We consider an effective lower bound of the Siegel–Tatuzawa type for general L-functions with three standard assumptions. We further assume three hypotheses in this paper that are essential in developing our argument. Under these assumptions and hypotheses, we prove a theorem of Siegel–Tatuzawa type for general L-functions. In particular, we prove such a theorem for symmetric power L-functions ...

The Analytic Class Number Formula and L-functions

On Siegel Disks of a Class of Entire Maps

Let f : C → C be an entire map of the form f(z) = P (z) exp(Q(z)), where P and Q are polynomials of arbitrary degrees (we allow the case Q = 0). Building upon a method pioneered by M. Shishikura, we show that if f has a Siegel disk of bounded type rotation number centered at the origin, then the boundary of this Siegel disk is a quasicircle containing at least one critical point of f . This uni...

Calculation of atomic number states

We analyse the conditions for producing atomic number states in a one-dimensional optical box using the Bethe ansatz method. This approach provides a general framework, enabling the study of number state production over a wide range of realistic experimental parameters. (Some figures in this article are in colour only in the electronic version)

A Class–field Theoretical Calculation

In this paper, we give the complete characterization of the p–torsion subgroups of certain idèle–class groups associated to characteristic p function fields. As an application, we answer a question which arose in the context of Tan’s approach [Ta1] to an important particular case of a generalization of a conjecture of Gross [Gro] on special values of L–functions. 1. Notation and motivation Let ...