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Define the Ramanujan theta function $f(a,b)$ as, $$f(a,b) = \sum_{n=-\infty}^{\infty} a^{n(n+1)/2}\,b^{n(n-1)/2}$$ and the Dedekind eta function, $$\eta(\tau) = q^{1/24}\prod_{n=1}^{\infty} ... 3answers 568 views ### Mock Theta Functions I am studying about Mock modular forms and Mock theta functions. I wonder how Zwegers connected mock theta functions with Harmonic Maass Forms? I mean, what was the philosophy/idea of Mock Theta ... 0answers 386 views ### Zero-free theta functions in the upper half plane Problem 1. Which full rank lattices \Lambda \subset \mathbb R^d have their corresponding theta function \theta_{\Lambda}(\tau):= \sum_{\bf n \in \Lambda } e^{\pi i \tau ||n||^2}  zero-free in ... 4answers 827 views ### Order of vanishing at the cusps for the modular theta function I am trying to examine the behavior of the theta function \theta(z)=\sum_{n\in\mathbb{Z}} e^{2\pi i n^2 z}, which is modular for \Gamma_0(4) of weight 1/2, at the cusps 0 and 1/2. My calculations ... 2answers 678 views ### What is the modern understanding of the order of a mock theta function? Ramanujan introduced mock theta functions and described them by an "order" which he did not define. As a result of the work of Zwegers and others we now have a better understanding of mock theta ... 2answers 1k views ### Relation between Theta series and Eisensteinseries In "Mackey - Unitary Group Representation in Physics, Probability and Number Theory" on page 326, George Mackey mentions a result of Ludwig Siegel, which was later generalized to semi-simple Lie ... 2answers 831 views ### Character of the Basic Representation for Affine E_8 in Terms of Jacobi Theta Functions When \mathfrak g is a complex, simple, simply laced Lie algebra of rank r then the (specialized) character of the basic representation for the corresponding affine Lie algebra \hat {\mathfrak g} ... 3answers 1k views ### How do modular forms of half-integral weight relate to the (quasi-modular) Eisenstein series? The Eisenstein series$$ G_{2k} = \sum_{(m,n) \neq (0,0)} \frac{1}{(m + n\tau)^{2k}}  are modular forms (if $k>1$) of weight $2k$ and quasi-modular if $k=1$. It is clear that given modular forms ...
So I am (barely) familiar with the construction of the theta function of an integral lattice $L$. The theta function, as I understand it, is defined as the function which takes a variable $z$ and ...