All Questions

For any $z \in \mathcal{H}$, let $q = e^{2\pi iz}$; and the eta function is defined as ${\displaystyle \eta (q) =q^{\frac {1}{24}}\prod _{n=1}^{\infty }\left(1-q^{n}\right).}$ By an $\eta$-quotient ...

One can attach $\ell$-adic Galois representations to holomorphic cuspidal newforms of weight $2$ on the upper half-plane. If a newform is $L^2$-normalized, can one extract its maximum value from the ...

You can see the parts after my questions in the boxes. I received the answer to my first question in the comments. I am confused about the definition of $a_n$ and $b_n$ in Part II below. I know the ...

I am studying the following Poincare-like series, \begin{equation} F_k(\tau,\bar{\tau})=\sum_{\gamma\in\Gamma_{\infty}\backslash\Gamma}\sqrt{\text{Im}\gamma\tau}(q_{\gamma}\bar{q}_{\gamma})^k, \end{...

Suppose that $\Gamma$ is a group acting discontinuously on $\mathcal{H} = \{ z \in \mathbb{C} : \operatorname{Im}(z) > 1\}$. In order to keep things simple, suppose that $\Gamma \subseteq \...

Siegel's formula(Siegel-Weil) directly relates the weighted sum of theta functions to Eisenstein series. (Or equivalently, the weighted sum of the cusp form is zero). I wonder if there is a ...