Displaying similar documents to “Hyperbolic lattice-point counting and modular symbols”

Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity

Enrico Bernardi, Antonio Bove, Vesselin Petkov (2010)

Journées Équations aux dérivées partielles

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We study a class of third order hyperbolic operators P in G = Ω { 0 t T } , Ω n + 1 with triple characteristics on t = 0 . We consider the case when the fundamental matrix of the principal symbol for t = 0 has a couple of non vanishing real eigenvalues and P is strictly hyperbolic for t > 0 . We prove that P is strongly hyperbolic, that is the Cauchy problem for P + Q is well posed in G for any lower order terms Q .

Unipotent vector bundles and higher-order non-holomorphic Eisenstein series

Jay Jorgenson, Cormac O’Sullivan (2008)

Journal de Théorie des Nombres de Bordeaux

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Higher-order non-holomorphic Eisenstein series associated to a Fuchsian group Γ are defined by twisting the series expansion for classical non-holomorphic Eisenstein series by powers of modular symbols. Their functional identities include multiplicative and additive factors, making them distinct from classical Eisenstein series. In this article we prove the meromorphic continuation of these series and establish their functional equations which relate values at s and 1 - s . In addition, we...

Artin formalism for Selberg zeta functions of co-finite Kleinian groups

Eliot Brenner, Florin Spinu (2009)

Journal de Théorie des Nombres de Bordeaux

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Let Γ 3 be a finite-volume quotient of the upper-half space, where Γ SL ( 2 , ) is a discrete subgroup. To a finite dimensional unitary representation χ of Γ one associates the Selberg zeta function Z ( s ; Γ ; χ ) . In this paper we prove the Artin formalism for the Selberg zeta function. Namely, if Γ ˜ is a finite index group extension of Γ in SL ( 2 , ) , and π = Ind Γ Γ ˜ χ is the induced representation, then Z ( s ; Γ ; χ ) = Z ( s ; Γ ˜ ; π ) . In the second part of the paper we prove by a direct method the analogous identity for the scattering function, namely φ ( s ; Γ ; χ ) = φ ( s ; Γ ˜ ; π ) ,...

Sigma order continuity and best approximation in L ϱ -spaces

Shelby J. Kilmer, Wojciech M. Kozƚowski, Grzegorz Lewicki (1991)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we give a characterization of σ -order continuity of modular function spaces L ϱ in terms of the existence of best approximants by elements of order closed sublattices of L ϱ . We consider separately the case of Musielak–Orlicz spaces generated by non- σ -finite measures. Such spaces are not modular function spaces and the proofs require somewhat different methods.