Results 11 to 20 of about 114 (98)
Dedekind's η-function and the cohomology of infinite dimensional Lie algebras [PDF]
Proceedings of the National Academy of Sciences, 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.
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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
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Evaluation of the Dedekind Eta Function [PDF]
Canadian Mathematical Bulletin, 2006 AbstractWe extend the methods of Van der Poorten and Chapman for explicitly evaluating the Dedekind eta function at quadratic irrationalities. Via evaluation of HeckeL-series we obtain new evaluations at points in imaginary quadratic number fields with class numbers 3 and 4.
Robin Chapman, William Hart
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Values of the Dedekind Eta Function at Quadratic Irrationalities [PDF]
Canadian Journal of Mathematics, 1999 AbstractLet d be the discriminant of an imaginary quadratic field. Let a, b, c be integers such that b2 − 4ac = d, a > 0, gcd(a, b, c) = 1.The value of |η(b + √d)/2a)| is determined explicitly, where η(z) is Dedekind’s eta ...
van der Poorten, Alfred +1 more
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Generalized Dedekind eta-functions and generalized Dedekind sums [PDF]
Transactions of the American Mathematical Society, 1973 A transformation formula under modular substitutions is derived for a very large class of generalized Eisenstein series. The result also gives a transformation formula for generalized Dedekind eta-functions. Various types of Dedekind sums arise, and reciprocity laws are established.
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ON A LATTICE GENERALISATION OF THE LOGARITHM AND A DEFORMATION OF THE DEDEKIND ETA FUNCTION [PDF]
Bulletin of the Australian Mathematical Society, 2020 We consider a deformation $E_{L,\unicode[STIX]{x1D6EC}}^{(m)}(it)$ of the Dedekind eta function depending on two $d$-dimensional simple lattices $(L,\unicode[STIX]{x1D6EC})$ and two parameters $(m,t)\in (0,\infty )$, initially proposed by Terry Gannon.
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Neutrino masses and mixing from double covering of finite modular groups
Journal of High Energy Physics, 2019 We extend the even weight modular forms of modular invariant approach to general integral weight modular forms. We find that the modular forms of integral weights and level N can be arranged into irreducible representations of the homogeneous finite ...
Xiang-Gan Liu, Gui-Jun Ding
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Polynomials Related to Powers of the Dedekind Eta Function
Integers, 2018 See the abstract in the attached pdf.
Heim, B. ; https://orcid.org/0000-0001-6644-8842 +1 more
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A conjectured analogue of Dedekind’s eta function for $K3$ surfaces [PDF]
Mathematical Research Letters, 1995 For \(\tau\in \mathbb{C}\) let \(E_\tau =\mathbb{C}/ \Lambda_\tau\) be the associated elliptic curve; the Dedekind's eta function \(\eta (\tau)\) provides a formula for the product of the non 0 eigenvalues of the Laplacian \(\Delta= -4b \partial^2/ \partial z \partial \overline z\). This theory has been extended to K3 surfaces, by means of a function \(
Jorgenson, Jay, Todorov, Andrey
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Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52
Open Mathematics, 2017 The convolution sum, ∑(l,m)∈N02αl+βm=nσ(l)σ(m), $ \begin{array}{} \sum\limits_{{(l\, ,m)\in \mathbb{N}_{0}^{2}}\atop{\alpha \,l+\beta\, m=n}} \sigma(l)\sigma(m), \end{array} $ where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms
Ntienjem Ebénézer
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