6 problems

Let $\phi_i$ be a Hecke–Maass cusp form with spectral parameter $\lm_i$, and let $d_i$ denote its associated triple period coefficient. For every $\eps>0$, the notation…

For an $L$-function $L(s,\pi)$ with analytic conductor $\mathcal{C}(\pi)$, a simultaneous eigenfunction property refers to the underlying modular form being a simultaneous eigenfun…

Test vector conjecture for local triple product periods. There exist unit vectors $\varphi_i\in\pi_i$ such that: (i) the Sobolev norms of $\varphi_3$ are controlled by $M$, namely,…

Let $N_1,N_2\geq 1$ be two integers. Let $k$ be an even integer and $t\geq 1$. Let $F$ be a normalized ${\rm GL}(3)$-Maass form of level $N_1$, and let $f$ be a ${\rm GL}(2)$-Maass…

Subconvexity conjecture. There exists $\delta>0$ such that

Subconvexity conjecture. Such a bound should always hold for some $\theta<\frac14$. This conjecture asks for an improvement over the convexity exponent and is a central problem in…