Results 1 to 10 of about 95 (83)
New proof to Somos’s Dedekind eta-function identities of level 10 [PDF]
Soft Computing, 2021 AbstractMichael Somos used PARI/GP script to generate several Dedekind eta-function identities by using computer. In the present work, we prove two new Dedekind eta-function identities of level 10 discovered by Somos in two different methods. Also during this process, we give an alternate method to Somos’s Dedekind eta-function identities of level 10 ...
B R Srivatsa Kumar +2 more
exaly +3 more sources
Dedekind's eta-function and the cohomology of infinite dimensional Lie algebras. [PDF]
Proc Natl Acad Sci U S A, 1975 We compute the cohomology of certain infinite dimensional Lie algebras which are subalgebras of Lie algebras introduced by Moody and Kac. We note a relation between our results and the cohomology of loop spaces of compact groups. Finally, we derive, by Euler-Poincaré, identities of Macdonald for powers of the Dedekind η-function.
Garland H.
europepmc +4 more sources
Records on the vanishing of Fourier coefficients of powers of the Dedekind eta function [PDF]
Research in Number Theory, 2018 13 ...
Bernhard Heim +2 more
exaly +4 more sources
Weight of a link in a shortest path tree and the Dedekind Eta function
Random Structures and Algorithms, 2010 AbstractThe weight of a randomly chosen link in the shortest path tree on the complete graph with exponential i.i.d. link weights is studied. The corresponding exact probability generating function and the asymptotic law are derived. As a remarkable coincidence, this asymptotic law is precisely the same as the distribution of the cost of one “job” in ...
Piet Van Mieghem
exaly +5 more sources
$G$-fixed Hilbert schemes on $K3$ surfaces, modular forms, and eta products [PDF]
Épijournal de Géométrie Algébrique, 2022 Let $X$ be a complex $K3$ surface with an effective action of a group $G$ which preserves the holomorphic symplectic form. Let $$ Z_{X,G}(q) = \sum_{n=0}^{\infty} e\left(\operatorname{Hilb}^{n}(X)^{G} \right)\, q^{n-1} $$ be the generating function for ...
Jim Bryan, Ádám Gyenge
doaj +1 more source
Reciprocity of poly-Dedekind-type DC sums involving poly-Euler functions
Advances in Difference Equations, 2021 The classical Dedekind sums appear in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group.
Yuankui Ma +4 more
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A Nekrasov-Okounkov type formula for affine $\widetilde{C}$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 In 2008, Han rediscovered an expansion of powers of Dedekind $\eta$ function due to Nekrasov and Okounkov by using Macdonald's identity in type $\widetilde{A}$.
Mathias Pétréolle
doaj +1 more source
Imaginary Powers of the Dedekind Eta Function [PDF]
Experimental Mathematics, 2018 In this article, complex powers of the Dedekind eta function are studied. The vanishing of the nth Fourier coefficients are labeled by the roots of an attached polynomial pn(x).
Heim, B. ; https://orcid.org/0000-0001-6644-8842 +2 more
openaire +2 more sources
Identities on poly-Dedekind sums
Advances in Difference Equations, 2020 Dedekind sums occur in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group. In 1892, Dedekind showed a reciprocity relation for the Dedekind sums.
Taekyun Kim +3 more
doaj +1 more source
Type III seesaw under $$A_4$$ A 4 modular symmetry with leptogenesis
European Physical Journal C: Particles and Fields, 2022 We make an attempt to study neutrino phenomenology in the framework of type-III seesaw by considering $$A_4$$ A 4 modular symmetry in the super-symmetric context.
Priya Mishra +3 more
doaj +1 more source