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Let us consider the case when the centre acts trivially, for simplicity. Let us call $H_p$ to be the polynomial algebra generated by the classical Hecke operators $\{T_{p^r}\mid r\ge 0\}$. Using the H …

For $(1)$, I believe the size would still be $\gg x^{1-\epsilon}$. However, if you allow $$\sum_{p\sim x} |A(p,1)|^2+A|(p^2,1)|^2$$ a lower bound of similar sort is obtained by Blomer-Maga's paper Cor …

Consider the cuspidal representation $\pi:=\pi_f\otimes\pi_\infty$ of $\mathrm{GL}_2(\mathbb{A})$ with the central character $\omega_\chi$, the Hecke character attached to $\chi$, such that $\pi_f$ ha …

I think this is fine. Indeed, $S$ as a function of $B$ is of negligible size. This can also be checked as follows. Using Mellin transform and absolute convergence of the Dirichlet series of $\lambda$ …

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 funct …