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Recently, P. C. Toh derived identities expressing theta series associated with fundamental idoneal discriminants in terms of generalized Lambert series. His method depends on the fact that the ring of integers of a number field is a Dedekind domain, and is not applicable to theta series associated with non-fundamental idoneal discriminants. The aim of this article is to devise methods for determining the generalized Lambert series representations of theta series associated with non-fundamental idoneal...

Theta Series of Imaginary Quadratic Function Fields.

Hans-Georg Rück (1995)

Manuscripta mathematica

Thetareihen und modulare Spitzenformen zu den Hilbertschen Modulgruppen reell-quadratischer Körper.

Carl Friedrich Hermann (1987)

Mathematische Annalen

Thetareihen und modulare Spitzenformen zu den Hilbertschen Modulgruppen reell-quadratischer Körper. II.

Carl Friedrich Hermann (1989)

Mathematische Annalen

Third symmetric power $L$ -functions for $G L (2)$

Freydoon Shahidi (1989)

Compositio Mathematica

Three problems for polynomials of small measure

Artūras Dubickas (2001)

Acta Arithmetica

Thue equations over algebraic function fields

Günter Lettl (2005)

Acta Arithmetica

Tilings associated with beta-numeration and substitutions.

Berthé, Valérie, Siegel, Anne (2005)

Integers

Tilings associated with non-Pisot matrices

Maki Furukado, Shunji Ito, E. Arthur Robinson (2006)

Annales de l’institut Fourier

Suppose $A \in G l_{d} (ℤ)$ has a 2-dimensional expanding subspace $E^{u}$ , satisfies a regularity condition, called “good star”, and has $A^{*} \geq 0$ , where $A^{*}$ is an oriented compound of $A$ . A morphism $θ$ of the free group on ${1, 2, \dots, d}$ is called a non-abelianization of $A$ if it has structure matrix $A$ . We show that there is a tiling substitution $Θ$ whose “boundary substitution” $θ = \partial Θ$ is a non-abelianization of $A$ . Such a tiling substitution $Θ$ leads to a self-affine tiling of $E^{u} \sim ℝ^{2}$ with $A_{u} {: = A |}_{E_{u}} \in G L_{2} (ℝ)$ as its expansion. In the last section we find conditions on $A$ so...

Tilings of the Square with Similar Rectangles.

G. Szekeres, M. Laczkovich (1995)

Discrete & computational geometry

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