Results 11 to 20 of about 229 (136)
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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New approach for Somos’s Dedekind eta-function identities of level 6
Proyecciones (Antofagasta), 2021 In the present work, we prove few new Dedekind eta-function identities of level 6 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 6 proved by B. R. Srivatsa Kumar et al. As an application of this, we establish colored partition identities.
D. Anu Radha +2 more
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Non-perturbative corrections in the semi-classical limit of double-scaled SYK
Journal of High Energy PhysicsWe study the disk partition function of double-scaled SYK model (DSSYK) in the small λ limit, where λ = log q is the coupling of DSSYK. We find that the partition function receives non-perturbative corrections in λ, which can be resummed by the cubic ...
Kazumi Okuyama
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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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Schlafli modular equations for generalized Weber functions [PDF]
, 2008 Sets of appropriately normalized eta quotients, that we call level n Weber functions, are defined, and certain identities generalizing Weber function identities are proved for these functions.
William B. Hart, Hart, William B.
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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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