Some Musings on Theta, Eta, and Zeta

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–).1. The author has published over 100 papers and several books.2. In 2013 he was inducted as a Fellow into the American Mathematical Society.

• 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.