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THE LIMIT MULTIPLICITY PROBLEM FOR CONGRUENCE SUBGROUPS OF ARITHMETIC LATTICES AND THE TRACE FORMULA (Automorphic Representations and Related Topics)

THE LIMIT MULTIPLICITY PROBLEM FOR CONGRUENCE SUBGROUPS OF ARITHMETIC LATTICES AND THE TRACE FORMULA (Automorphic Representations and Related Topics)
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Results and problems on congruence lattice representations

Algebra universalis, 2006
We survey some results and problems on congruence lattice representations. We will consider congruence representations and similarity type, and we will consider simultaneous congruence representations. A seemingly innocuous problem unites the sections.
William A. Lampe
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A constructive approach to the finite congruence lattice representation problem

Algebra Universalis, 2000
A finite lattice is representable if it is isomorphic to the congruence lattice of a finite algebra. The author develops methods by which one can construct new representable lattices from known ones. The main results: Theorem 4.2. Every finite lattice which contains no 3-element antichains is representable. Theorem 5.1. Let \(A\) be a finite set. There
J. Snow
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An Improvement of the Congruence Solver of Lattice Isomorphism Problem over Totally Real Number Fields and Applications

International Conference on Cryptology in Africa
Nour-eddine Rahmani, Taoufik Serraj, Moulay Chrif Ismaili   +2 more
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Existence and Congruence of Global Attractors for Damped and Forced Integrable and Nonintegrable Discrete Nonlinear Schrödinger Equations

Journal of Dynamics and Differential Equations, 2021
We study two damped and forced discrete nonlinear Schrödinger equations on the one-dimensional infinite lattice. Without damping and forcing they are represented by the integrable Ablowitz-Ladik equation (AL) featuring non-local cubic nonlinear terms ...
D. Hennig
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Some preliminary results on the set of principal congruences of a finite lattice

Algebra Universalis, 2017
In the second edition of the congruence lattice book, Problem 22.1 asks for a characterization of subsets Q of a finite distributive lattice D such that there is a finite lattice L whose congruence lattice is isomorphic to D and under this isomorphism Q ...
G. Grätzer, H. Lakser
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Lattice Security Analysis Algorithms for the Quadratic Congruence Outsourcing Scheme in IoT

IEEE Internet of Things Journal
Designing secure outsourcing schemes enables resource-constrained Internet of Things (IoT) devices to perform highly complex computational tasks. Solving the quadratic congruence problem is one of the core components in the construction of cryptographic ...
Ran Zhang, J. Bi, Lixiang Li, Haipeng Peng   +3 more
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On the Decision Problem of the Congruence Lattices of Pseudocomplemented Semilattices( )

1977
Publisher Summary This chapter focuses on the decision problem of the congruence lattices of pseudocomplemented semilattices. The essential undecidability of the theories of closure algebras, Brouwerian algebras, the algebras of bodies, the algebras of convexity, and the semi-projective algebra are discussed in the chapter.
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2345. A lattice problem

Mathematical Gazette, 1953
E. Newbery
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The Congruence Lattice and the Automorphism Group

, 2016
G. Grätzer
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