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Traces in Arithmetic Fuchsian Groups

โœ Scribed by Stefan Johansson

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
397 KB
Volume
66
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

Let A be a quaternion algebra over an algebraic number field F of degree n over

the set of traces of the elements in O 1 and T O (r)=[t # T O : 0 t 2r]. The first purpose of this paper is to show that lim r ร„ |T O (r)| r = 2 2n&1 -D F p | d(O) m p (O), where D F is the discriminant of F, d(O) is the (reduced) discriminant of O, and m p (O) only depends on the completion O p of O for nonzero prime ideals p dividing d(O). We also calculate the invariants m p (O) for important families of orders.

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