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Related papers: Singular values of generalized $\lambda$ functions

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We extend Norton-Borcherds-Koike's replication formulae to super-replicable ones by working with the congruence groups $\Gamma_1(N)$ and find the product identities which characterize super-replicable functions. These will provide a clue…

Number Theory · Mathematics 2007-05-23 Chang Heon Kim , Ja Kyung Koo

One may consider the generalization of Jacobi polynomials and the Jacobi function of the second kind to a general function where the index is allowed to be a complex number instead of a non-negative integer. These functions are referred to…

Classical Analysis and ODEs · Mathematics 2023-08-29 Howard S. Cohl , Roberto S. Costas-Santos

We introduce the notion of the generalized-analytical function of the poly-number variable, which is a non-trivial generalization of the notion of analytical function of the complex variable and, therefore, may turn out to be fundamental in…

Mathematical Physics · Physics 2007-05-23 G. I. Garasko

We introduce and solve an infinite class of loop integrals which generalises the well-known ladder series. The integrals are described in terms of single-valued polylogarithmic functions which satisfy certain differential equations. The…

High Energy Physics - Theory · Physics 2015-06-05 J. M. Drummond

Consider exponential Carmichael function $\lambda^{(e)}$ such that $\lambda^{(e)}$ is multiplicative and $\lambda^{(e)}(p^a) = \lambda(a)$, where $\lambda$ is usual Carmichael function. We discuss the value of $\sum \lambda^{(e)}(n)$, where…

Number Theory · Mathematics 2014-05-30 Andrew V. Lelechenko

We prove an estimate for spherical functions $\varphi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian…

Representation Theory · Mathematics 2022-07-01 Xiaocheng Li

Let $\boldsymbol{\Lambda}\,(=\mathbb{F}^{n^{3}})$, where $\mathbb{F}$ is a field with $|\mathbb{F}|>2$, be the space of structure vectors of algebras having the $n$-dimensional $\mathbb{F}$-space $V$ as the underlying vector space. Also let…

Rings and Algebras · Mathematics 2020-08-05 Christakis A. Pallikaros , Harold N. Ward

We show that for any finite-dimensional algebra $\Lambda$ of infinite representation type, over a perfect field, there is a bounded principal ideal domain $\Gamma$ and a representation embedding from $\Gamma -$mod into $\Lambda -$mod. As an…

Representation Theory · Mathematics 2024-06-24 Raymundo Bautista Ramos , Jesús Efrén Pérez Terrazas , Leonardo Salmerón Castro

We develop a calculus based on graph enumeration for $S_n$-equivariant motivic invariants of graphically stratified moduli spaces. We apply our theory to the Deligne--Mumford moduli space $\overline{\mathcal{M}}_{g, n}$ and to the space of…

Algebraic Geometry · Mathematics 2025-10-09 Siddarth Kannan , Terry Dekun Song

In this paper, we will apply the tools from number theory and modular forms to the study of the Seiberg-Witten theory. We will express the holomorphic functions $a, a_D$, which generate the lattice $Z=n_e a+n_m a_D, (n_e, n_m) \in…

High Energy Physics - Theory · Physics 2021-01-14 Wenzhe Yang

We extend the Colombeau algebra of generalized functions to arbitrary (infinitely differentiable, paracompact) n-dimensional manifolds M. Embedding of continuous functions and distributions is achieved with the help of a family of n-forms…

General Relativity and Quantum Cosmology · Physics 2007-05-23 H. Balasin

We study equivariant modules over $GL(V)$ over the polynomial ring $R = Sym V$. We introduce for every partition $\lambda$ the elementary equivariant module $M_{\lambda}$. Then we prove that any finitely generated equivariant module admits…

Commutative Algebra · Mathematics 2014-10-03 Mikhail Gudim

The singularities of the $\Gamma$ function, a meromorphic function on the complex plane, are known to occur at the nonpositive integers. We show, using Euler and Gauss identities, that for all positive integers $n$ and $k$, $$…

General Mathematics · Mathematics 2010-08-16 Anirudh Prabhu

A further significant extension is presented of the infinitely large class of differential algebras of generalized functions which are the basic structures in the nonlinear algebraic theory listed under 46F30 in the AMS Mathematical Subject…

General Mathematics · Mathematics 2010-06-29 Elemer E Rosinger

Let G be the group of points of a quasi-split reductive algebraic group over a local field F. It follows from the local Langlands conjectures that to every non-trivial additive character of F and every representation of the Langlands dual…

Algebraic Geometry · Mathematics 2007-05-23 Alexander Braverman , David Kazhdan , V. Vologodsky

There is a natural conjugation action on the set of endomorphism of $\P^N$ of fixed degree $d \geq 2$. The quotient by this action forms the moduli of degree $d$ endomorphisms of $\P^N$, denoted $\mathcal{M}_d^N$. We construct invariant…

Dynamical Systems · Mathematics 2019-08-09 Benjamin Hutz

The convergence of double Fourier series of functions of bounded partial $\Lambda$-variation is investigated. The sufficient and necessary conditions on the sequence $\Lambda=\{\lambda_n\}$ are found for the convergence of Fourier series of…

Analysis of PDEs · Mathematics 2012-10-17 Ushangi Goginava , Artur Sahakian

In this paper we present a semantics for a linear algebraic lambda-calculus based on realizability. This semantics characterizes a notion of unitarity in the system, answering a long standing issue. We derive from the semantics a set of…

Logic in Computer Science · Computer Science 2019-12-06 Alejandro Díaz-Caro , Mauricio Guillermo , Alexandre Miquel , Benoît Valiron

Let $\Lambda$ be an $n$-Auslander algebra with global dimension $n+1$. In this paper, we prove that $\Lambda$ is representation-finite if and only if the number of non-isomorphic indecomposable $\Lambda$-modules with projective dimension…

Representation Theory · Mathematics 2023-08-22 Shen Li

We study Measurable Imbeddability between groups, which is an order-like generalization of Measure Equivalence that allows the imbedded group to have an infinite measure fundamental domain. We prove if $\Lambda_1$ measurably imbeds into…

Group Theory · Mathematics 2024-03-29 Özkan Demir
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