Some Musings on Theta Eta and Zeta

<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 author���s 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 Schr��dinger 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 Szekeres���Szafron 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>