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2017 Zeta functions and ideal classes of quaternion orders
Jonathan W. Sands
Rocky Mountain J. Math. 47(4): 1277-1300 (2017). DOI: 10.1216/RMJ-2017-47-4-1277

Abstract

Inspired by Stark's analytic proof of class number finiteness of a ring of integers in an algebraic number field, we give a new proof of the finiteness of the number of classes of ideals in a maximal order of a totally definite quaternion algebra over a totally real number field. Our proof makes use of Epstein zeta function properties. This approach leads to alternative proofs of Eichler's mass formula and even parity of the number of ramified primes in the quaternion algebra.

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Jonathan W. Sands. "Zeta functions and ideal classes of quaternion orders." Rocky Mountain J. Math. 47 (4) 1277 - 1300, 2017. https://doi.org/10.1216/RMJ-2017-47-4-1277

Information

Published: 2017
First available in Project Euclid: 6 August 2017

zbMATH: 06790014
MathSciNet: MR3689954
Digital Object Identifier: 10.1216/RMJ-2017-47-4-1277

Subjects:
Primary: 11R52
Secondary: 11E12, 11E45, 16H10

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 4 • 2017
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