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Some Musings on Theta, Eta, and Zeta From E8 to Cold Plasma to an lnhomogeneous Universe /

This book continues the applications of mathematics, more specifically of theta, eta, and zeta functions, and modular forms, to various areas of theoretical physics. It is a follow-up and extension in some sense of the author’s earlier book entitled A window into zeta and modular physics. Some of th...

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Bibliographic Details
Main Author: Williams, Floyd L. (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:English
Published: Singapore : Springer Nature Singapore : Imprint: Springer, 2023.
Edition:1st ed. 2023.
Series:Mathematical Physics Studies,
Subjects:
Mathematical physics.
Number theory.
General relativity (Physics).
Mathematical Physics.
Number Theory.
General Relativity.
Online Access:https://doi.org/10.1007/978-981-99-5336-3
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Table of Contents:
  • A Theta Function Attached to a Positive Definite Matrix
  • Jacobi Type Inversion Formulas
  • A Theorem of Minkowski: Enter E8
  • Modular Properties of Theta and Eta
  • An Epstein Zeta Function Attached to A
  • An Inhomogeneous Epstein Zeta Function
  • Dirichlet and Hecke L-functions, Sums of Squares, and Some Other Stuff
  • The Modular j-Invariant and Powers of Its Cube Root: Enter E8 Again
  • Modular Forms of Non-Positive Weight: Exact Formulas and Asymptotics of Their Fourier Coefficients
  • More on Logarithmic Corrections to Black Hole Entropy
  • A Dedekind Type Eta Function Attached to the Hecke Group Γ0(N)
  • Elementary Particles, the E8 Root Lattice, and a Patterson-Selberg Zeta Function
  • The Uncontroversial Mathematics Behind Garrett Lisi’s Controversial “Theory of Every
  • The Elliptic Functions sn(x, κ), cn(x, κ), and dn(x, κ) of C.Jacobi
  • The Continuous Heisenberg Model, Reaction Diffusion System, Cold Plasma, and the J-T Black Hole
  • The Weierstrass P-Function and Some KdV Solutions
  • The Weierstrass Sigma and Zeta Functions: Theta Function Connections
  • A Finite Temperature Zeta Function
  • Lemaitre, Inhomogeneous Cosmology, and a Quick Look at the BTZ Black Hole
  • A Cold Plasma-sine-Gordon Connection
  • A Theta and Zeta Function Attached to a Non- Compact Symmetric Space: Computation of the One-Loop Effective Potential.

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