On the Complete Evaluation of Jacobi Theta Functions
Using numerical, theoretical and general methods, we construct evaluation formulas for the Jacobi $θ$ functions. Some of our results are conjectures, but are verified numerically.
math.GM↗
arXiv subjects
N. D. Bagis
Publications and source records attributed to N. D. Bagis.
Properties of Lerch Sums and Ramanujan's Mock Theta Functions
In this article we study properties of Ramanujan's mock theta functions that can be expressed in Lerch sums. We mainly show that each Lerch sum is actually the integral of a Jacobian theta function (here we show that for $\vartheta_3(t,q)$ and $\vartheta_4(t,q)$) and the $\sec-$function. We also prove some modular relations and evaluate the Fourier coefficients of a class of Lerch sums.
math.GM↗
Evaluations of certain theta functions in Ramanujan theory of alternative modular bases
We give evaluations of certain Borwein's theta functions which appear in Ramanujan theory of alternative elliptic modular bases. Most of this theory where developed by B.C. Berndt, S. Bhargava and F.G. Garvan. We also study the most general class of these theta functions and give evaluation theorems and conjectures.
math.GM↗