On generators of arithmetic groups over function fields

Mihran Papikian

doi:10.1142/S1793042111004265

On generators of arithmetic groups over function fields

Mihran Papikian

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let F = _q(T) be the field of rational functions with _q-coefficients, and A = _q[T] be the subring of polynomials. Let D be a division quaternion algebra over F which is split at 1/T. For certain A-orders in D we find explicit finite sets generating their groups of units.

Original language	English (US)
Pages (from-to)	1573-1587
Number of pages	15
Journal	International Journal of Number Theory
Volume	7
Issue number	6
DOIs	https://doi.org/10.1142/S1793042111004265
State	Published - Sep 2011

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1142/S1793042111004265

Cite this

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title = "On generators of arithmetic groups over function fields",

abstract = "Let F = q(T) be the field of rational functions with q-coefficients, and A = q[T] be the subring of polynomials. Let D be a division quaternion algebra over F which is split at 1/T. For certain A-orders in D we find explicit finite sets generating their groups of units.",

author = "Mihran Papikian",

note = "Funding Information: The work on this paper was started while I was visiting the Department of Mathematics of Saarland University. I thank the members of the department for their warm hospitality. I thank R. Butenuth and E.-U. Gekeler for stimulating discussions. The author was supported in part by NSF grant DMS-0801208 and Humboldt Research Fellowship.",

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N2 - Let F = q(T) be the field of rational functions with q-coefficients, and A = q[T] be the subring of polynomials. Let D be a division quaternion algebra over F which is split at 1/T. For certain A-orders in D we find explicit finite sets generating their groups of units.

AB - Let F = q(T) be the field of rational functions with q-coefficients, and A = q[T] be the subring of polynomials. Let D be a division quaternion algebra over F which is split at 1/T. For certain A-orders in D we find explicit finite sets generating their groups of units.

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On generators of arithmetic groups over function fields

Abstract

All Science Journal Classification (ASJC) codes

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