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001483987 001__ 1483987
001483987 003__ OCoLC
001483987 005__ 20240117003309.0
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001483987 019__ $$a1407336769$$a1407346775
001483987 020__ $$a9789819953363$$q(electronic bk.)
001483987 020__ $$a9819953367$$q(electronic bk.)
001483987 020__ $$z9819953359
001483987 020__ $$z9789819953356
001483987 0247_ $$a10.1007/978-981-99-5336-3$$2doi
001483987 035__ $$aSP(OCoLC)1409031193
001483987 040__ $$aEBLCP$$beng$$cEBLCP$$dYDX$$dGW5XE$$dOCLKB$$dOCLCO$$dYDX$$dOCLCO
001483987 049__ $$aISEA
001483987 050_4 $$aQC20$$b.W555 2023
001483987 08204 $$a530.15$$223/eng/20231113
001483987 1001_ $$aWilliams, Floyd L.
001483987 24510 $$aSome musings on Theta, Eta, and Zeta :$$bfrom E8 to cold plasma to an Inhomogeneous universe /$$cFloyd L. Williams.
001483987 260__ $$aSingapore :$$bSpringer,$$c2023.
001483987 300__ $$a1 online resource (233 p.).
001483987 336__ $$atext$$btxt$$2rdacontent
001483987 337__ $$acomputer$$bc$$2rdamedia
001483987 338__ $$aonline resource$$bcr$$2rdacarrier
001483987 4901_ $$aMathematical Physics Studies
001483987 504__ $$aIncludes bibliographical references.
001483987 5050_ $$aIntro -- Preface -- Contents -- 1 A Theta Function Attached to a Positive Definite Matrix -- 2 Jacobi Type Inversion Formulas -- 3 A Theorem of Minkowski: Enter E8 -- 4 Modular Properties of Theta and Eta -- 5 An Epstein Zeta Function Attached to A -- 6 An Inhomogeneous Epstein Zeta Function -- 7 Dirichlet and Hecke L-Functions, Sums of Squares, and Some Other Stuff -- 8 The Modular j-Invariant and Powers of Its Cube Root: Enter E8 Again -- 9 Modular Forms of Non-positive Weight: Exact Formulas and Asymptotics of Their Fourier Coefficients
001483987 5058_ $$a15 The Continuous Heisenberg Model, Reaction Diffusion System, Cold Plasma, and the J-T Black Hole -- 16 The Weierstrass mathcalP-Function and Some KdV Solutions -- 17 The Weierstrass Sigma and Zeta Functions: Theta Function Connections -- 18 A Finite Temperature Zeta Function -- 19 Lemaitre, Inhomogeneous Cosmology, and a Quick Look at the BTZ Black Hole -- 20 A Cold Plasma-Sine-Gordon Connection -- 21 A Theta and Zeta Function Attached to a Non-compact Symmetric Space: Computation of the One-Loop Effective Potential -- Appendix References -- References
001483987 506__ $$aAccess limited to authorized users.
001483987 520__ $$aThis 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 authors earlier book entitled A window into zeta and modular physics. Some of the main topics are 1. A new approach to logarithmic corrections to black hole entropy 2. My recent work that provides for an explicit cold plasma-black hole connection 3. Generalization of work of physicists on certain asymptotic problems relating to string theory, for example, by way of the general theory of modular forms of non-positive weight 4. A construction of the E8 root lattice, its theta function, and its relevance for heterotic string theory 5. Applications of elliptic functions to KdV, nonlinear Schrdinger, and Duffing equations, for example, including a discussion of Lax pairs and the Miura transformation 6. Finite temperature zeta functions and partition functions for quantum fields in thermal equilibrium on various curved background spacetimes 7. Exact solutions of the Einstein gravitational field equations for Lemaitre and inhomogeneous cosmological models, with a special focus on the SzekeresSzafron exact solutions by way of the Weierstrass elliptic function 8. Elementary particles and my zeta function formula for higher spin fermionic particles; this covers, in particular, the gravitino particle (of spin 3/2) and bosons with integral spin s = 2, 3, 4, 5. These are some sample topics. Others include the continuous Heisenberg model, reaction diffusion systems, Dirichlet and Hecke L-functions, the modular j-invariant, the computation of the one-loop effective potential for non-compact symmetric spaces, the BTZ black hole, Jacobi inversion formulas, etc. Thus, there is a very large range of material with the first 9 chapters of preliminary, expositional background for mathematicians and physicists.
001483987 588__ $$aDescription based on print version record.
001483987 650_0 $$aMathematical physics.
001483987 650_0 $$aFunctions, Zeta.
001483987 650_0 $$aFunctions, Theta.
001483987 650_6 $$aPhysique mathématique.
001483987 650_6 $$aFonctions zêta.
001483987 650_6 $$aFonctions thêta.
001483987 655_0 $$aElectronic books.
001483987 77608 $$iPrint version:$$aWilliams, Floyd L.$$tSome Musings on Theta, Eta, and Zeta$$dSingapore : Springer Singapore Pte. Limited,c2023$$z9789819953356
001483987 830_0 $$aMathematical physics studies.
001483987 852__ $$bebk
001483987 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-981-99-5336-3$$zOnline Access$$91397441.1
001483987 909CO $$ooai:library.usi.edu:1483987$$pGLOBAL_SET
001483987 980__ $$aBIB
001483987 980__ $$aEBOOK
001483987 982__ $$aEbook
001483987 983__ $$aOnline
001483987 994__ $$a92$$bISE