A prime geodesic theorem for SL4

Deitmar, Anton; Pavey, Mark

doi:10.1007/s10455-007-9078-4

Cited by 14 publications

(21 citation statements)

References 44 publications

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“…This approach let to the conclusion that the error term O x . Regarding the corresponding results in [16], [3] and [13], it is enough to replace 3 4 by 1 − 1 2D in the final form of the prime geodesic theorem.…”

Section: Remarksmentioning

confidence: 99%

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On Some Classical andWeighted Estimates for SL4

Gusic

2020

Wseas Transactions on Systems and Control

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The purpose of this paper is two-sided. First, we obtain the correct estimate of the error term in the classical prime geodesic theorem for compact symmetric space SL4. As it turns out, the corrected error term depends on the degree of a certain polynomial appearing in the functional equation of the attached zeta function. This is in line with the known result in the case of compact Riemann surface, or more generally, with the corresponding result in the case of compact locally symmetric spaces of real rank one. Second, we derive a weighted form of the theorem. In particular, we prove that the aforementioned error term can be significantly improved when the classical approach is replaced by its higher level analogue.

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Section: Remarksmentioning

confidence: 99%

“…In [3] and [16], the authors derived two main results: a length spectrum for compact symmetric spaces represented as quotients of the Lie group SL 4 (R), and its application in totally quartic fields with no real quadratic subfield.…”

Section: Introductionmentioning

confidence: 99%

On Some Classical andWeighted Estimates for SL4

Gusic

2020

Wseas Transactions on Systems and Control

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“…We recall from the proof of Lemma 1.4 that θ([γ ]) is an order in the field Q(ae iθ , a −1 e iφ ). By Lemma 2.10 of [12] we have that trσ (γ ) = 4(1 − cos 2θ)(1 − cos 2φ). Let…”

Section: Lemma 27 Let [γ ] ∈ Ementioning

confidence: 99%

Class numbers of orders in complex quartic fields

Deitmar¹,

Pavey²

2007

Math. Ann.

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“…Motivated by the fact that the classical Selberg zeta function [17] is an entire function of order two and following Park's method [13] on hyperbolic manifolds with cusps, Avdispahić and Gušić [2] derived an analogous result for the zeta functions described in [5]. The main purpose of this paper is to give yet another proof of the result [2] based on Pavey's approach [14] in the quartic fields setting (see also, [8]).…”

Section: Introductionmentioning

confidence: 96%