✦ LIBER ✦

Theta Series of Quaternion Algebras over Function Fields

✍ Scribed by Holly J. Rosson

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 227 KB
Volume: 94
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2001.2723

No coin nor oath required. For personal study only.

✦ Synopsis

Let K be the function field over a finite field of odd order, and let H be a definite quaternion algebra over K. If L is an order of level M in H, we define theta series for each ideal I of L using the reduced norm on H. Using harmonic analysis on the completed algebra H . and the arithmetic of quaternion algebras, we establish a transformation law for these theta series. We also define analogs of the classical Hecke operators and show that in general, the Hecke operators map the theta series to a linear combination of theta series attached to different ideals, a generalization of the classical Eichler Commutation Relation.

📜 SIMILAR VOLUMES

Theta Functions with Harmonic Coefficien

Theta Functions with Harmonic Coefficients over Number Fields

✍ Olav K. Richter 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 196 KB

We investigate theta functions attached to quadratic forms over a number field K. We establish a functional equation by regarding the theta functions as specializations of symplectic theta functions. By applying a differential operator to the functional equation, we show how theta functions with har

Crossed Products over Algebraic Function

Crossed Products over Algebraic Function Fields

✍ B. Fein; M. Schacher 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 484 KB

E-Algebraic Functions over Fields of Pos

E-Algebraic Functions over Fields of Positive Characteristic—An Analogue of Differentially Algebraic Functions

✍ Habib Sharif 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 158 KB

A function or a power series f is called differentially algebraic if it satisfies a Ž X Ž n. . differential equation of the form P x, y, y , . . . , y s 0, where P is a nontrivial polynomial. This notion is usually defined only over fields of characteristic zero and is not so significant over fields

Partial Zeta Functions of Algebraic Vari

Partial Zeta Functions of Algebraic Varieties over Finite Fields

✍ Daqing Wan 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 147 KB

## DEDICATED TO PROFESSOR CHAO KO ON THE OCCASION OF HIS 90TH BIRTHDAY Motivated by arithmetic applications, we introduce the notion of a partial zeta function which generalizes the classical zeta function of an algebraic variety de"ned over a "nite "eld. We then explain two approaches to the gene

Representations of division algebras ove

Representations of division algebras over local fields

✍ Lawrence Corwin 📂 Article 📅 1974 🏛 Elsevier Science 🌐 English ⚖ 497 KB

Levels of Function Fields of Surfaces ov

Levels of Function Fields of Surfaces over Number Fields

✍ U. Jannsen; R. Sujatha 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 87 KB

We study the level of nonformally real function fields of surfaces over number fields and show that it is at most 4 for a large class of surfaces.  2002 Elsevier Science (USA) The level of a field F is the least integer n such that -1 is expressible as a sum of n squares in F. If -1 is not a sum o