On the Arithmetic and Geometry of Quaternion Algebras: A spectral correspondence for Maass waveforms
Item
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Title
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On the Arithmetic and Geometry of Quaternion Algebras: A spectral correspondence for Maass waveforms
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Identifier
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d_2009_2013:6544d86a1782:10835
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identifier
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11203
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Creator
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Blackman, Terrence Richard,
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Contributor
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Stefan Lemurell
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Date
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2011
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics | Applied mathematics | Arithmetic Fuchsian groups | Jacquet-Langlands correspondence | Maass newforms | Selberg Trace Formula
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Abstract
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Let A be an indefinite rational division quaternion algebra with discriminant d equal to pq where p and q are primes such that p, q > 2 and let Opq be a maximal order in A . Further, let Opq,p2r q2s , r, s ≥ 1 be an order of index p 2rq2 s in Opq with Eichler invariant equal to negative one at p and at q. Finally, let O1pq,p2 rq2s be the cocompact Fuchsian group given as the group of units of norm one in Opq,p2r q2s . Using the classical Selberg trace formula, we show that the positive Laplace eigenvalues, including multiplicities, for Maass forms on O1pq,p2 rq2s coincide with the Laplace spectrum for Maass newforms defined on the Hecke congruence group Gamma0(M) where, M, the level of the congruence group, is equal to p 2r+1q 2s+1, i.e., the discriminant of Opq,p2r q2s .
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Type
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dissertation
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Source
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2009_2013.csv
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degree
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Ph.D.
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Program
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Mathematics
