Titlebook: Some Musings on Theta, Eta, and Zeta; From E8 to Cold Plas Floyd L. Williams Book 2023 The Editor(s) (if applicable) and The Author(s), und

ANTIC

A Finite Temperature Zeta Function,.) can be expressed in terms of a ., which in turn is given as a Euclidean path integral—in the Feynman formulation. Details of these matters are presented in Chaps. 13, 14 of [108], for example. We consider here, for example, the quantized harmonic oscillator with frequency ., where the density mat

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Lemaitre, Inhomogeneous Cosmology, and a Quick Look at the BTZ Black Hole,m 1927 to 1931. Earlier work of the Russian mathematician (and meteorologist) Alexander Friedmann (1888–1925) in 1922 actually described a closed, expanding model. Lemaitre however connected the expansion with the redshift of galaxies (the Doppler effect), which by way of careful observations of Edw

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Modular Forms of Non-positive Weight: Exact Formulas and Asymptotics of Their Fourier Coefficients,or forms of weight zero there is also an exact formula for their Fourier coefficients—due to Brisebarre and Philibert [13]. These exact formulsectas are reviewed, along with some asymptotics of Fourier coefficients.

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The Continuous Heisenberg Model, Reaction Diffusion System, Cold Plasma, and the J-T Black Hole,ational field equations is expressed directly in terms of the . Ricci scalar curvature of .. By way of ., the Heisenberg model and the reaction diffusion system are guage equivalent. Thus a set of intertwining, connective ideas will play out.

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,The Weierstrass ,-Function and Some KdV Solutions, plethora of applications in other areas as well including nonlinear optics. This equation also has a cosmological connection as it appears in various scenarios including that of an inflationary universe [73]. J.D’ Amboise’s lecture in [33] deals with applications of elliptic and theta functions for a FRLW universe.

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Some Musings on Theta, Eta, and Zeta978-981-99-5336-3Series ISSN 0921-3767 Series E-ISSN 2352-3905

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FECK

A Dedekind Type Eta Function Attached to the Hecke Group , . is called a . of the first kind. To each cusp . of ., L. Goldstein in [47, 48] has attached a Dedekind type eta function . on . and, among other results, he has obtained an appropriate corresponding ..