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We study the infinitesimal generator of the Lax-Phillips semigroup of the automorphic scattering system defined on the Poincaré upper half-plane for SL₂(ℤ). We show that its spectrum consists only of the poles of the resolvent of the generator, and coincides with the poles of the scattering matrix, counted with multiplicities. Using this we construct an operator whose eigenvalues, counted with algebraic multiplicities (i.e. dimensions of generalized eigenspaces), are precisely the non-trivial zeros...

The logarithm of the Siegel function

Daniel S. Kubert (1978)

Compositio Mathematica

The module of vector-valued modular forms is Cohen-Macaulay

Richard Gottesman (2020)

Czechoslovak Mathematical Journal

Let $H$ denote a finite index subgroup of the modular group $Γ$ and let $ρ$ denote a finite-dimensional complex representation of $H .$ Let $M (ρ)$ denote the collection of holomorphic vector-valued modular forms for $ρ$ and let $M (H)$ denote the collection of modular forms on $H$ . Then $M (ρ)$ is a $ℤ$ -graded $M (H)$ -module. It has been proven that $M (ρ)$ may not be projective as a $M (H)$ -module. We prove that $M (ρ)$ is Cohen-Macaulay as a $M (H)$ -module. We also explain how to apply this result to prove that if $M (H)$ is a polynomial ring, then $M (ρ)$ is a free...

The polynomial $x^{3} + x^{2} + x - 1$ and elliptic curves of conductor 11

Alfred J. Van der Poorten (1976/1977)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

The spt-crank for overpartitions

Frank G. Garvan, Chris Jennings-Shaffer (2014)

Acta Arithmetica

Bringmann, Lovejoy, and Osburn (2009, 2010) showed that the generating functions of the spt-overpartition functions $\bar{s p t} (n)$ , ${\bar{s p t}}_{1} (n)$ , ${\bar{s p t}}_{2} (n)$ , and M2spt(n) are quasimock theta functions, and satisfy a number of simple Ramanujan-like congruences. Andrews, Garvan, and Liang (2012) defined an spt-crank in terms of weighted vector partitions which combinatorially explain simple congruences modulo 5 and 7 for spt(n). Chen, Ji, and Zang (2013) were able to define this spt-crank in terms of ordinary partitions. In this...

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Displaying 1 – 17 of 17

The Action of the Canonical Involution on Modular Forms of Weight 2 on ...0 (M).

The constant term of the cubic theta series.

The Equations for Modular Function Fields of Principal congruence subgroups of prime level.

The Group of Automorphisms of the Modular Function Field.

The Index of Stickelberger Ideals of Order2 and Cuspidal Class Numbers .

The laplacian operator on a Riemann surface

The laplacian operator on a Riemann surface, II

The laplacian operator on a Riemann surface, III

The Lax-Phillips infinitesimal generator and the scattering matrix for automorphic functions

The logarithm of the Siegel function

The module of vector-valued modular forms is Cohen-Macaulay

The polynomial $x^{3} + x^{2} + x - 1$ and elliptic curves of conductor 11

The spt-crank for overpartitions

The structure of totally disconnected, locally compact groups.

The zeros of certain Poincaré series

Theta Functions and Symplectic Groups.

Transzendente Zahlen als Fourierkoeffizienten von Heckes Modulformen

Currently displaying 1 – 17 of 17