Some Musings on Theta, Eta, and Zeta

Zusatztext

<p>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 authors earlier book entitled A window into zeta and modular physics. Some of the main topics are</p><p>1. A new approach to logarithmic corrections to black hole entropy</p><p>2. My recent work that provides for an explicit cold plasma-black hole connection</p><p>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</p><p>4. A construction of the E8 root lattice, its theta function, and its relevance for heterotic string theory</p><p>5. Applications of elliptic functions to KdV, nonlinear Schrödinger, and Duffing equations, for example, including a discussion of Lax pairs and the Miura transformation</p><p>6. Finite temperature zeta functionsand partition functions for quantum fields in thermal equilibrium on various curved background spacetimes</p><p>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</p><p>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<i>s</i> = 2, 3, 4, 5.</p><p>These are some sample topics. Others include the continuous Heisenberg model, reaction diffusion systems, Dirichlet and Hecke<i>L</i>-functions, the modular<i> j</i>-invariant, the computation of the one-loop effective potential for non-compact symmetric spaces, the BTZ black hole, Jacobi inversion formulas, etc.</p><p>Thus, there is a very large range of material with the first 9 chapters of preliminary, expositional background for mathematicians and physicists.</p>

Autorenportrait

<div>Professor Floyd L. Williams obtained his Ph.D. Mathematics in 1972. He held the positions of Associate Instructor at the University of California/Irvine (1970¿72) and Instructor Massachusetts Institute of Technology (1972¿75). At the University of Massachusetts-Amherst, the author has been Assistant Professor (1975¿1978), Associate Professor (1978¿84), and Professor (1984¿). </div> 1. The author has published over 100 papers and several books. <div>2. In 2013 he was inducted as a Fellow into the American Mathematical Society.</div>

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