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Hybrid sup-norm bounds for Maass newforms of powerful level
(Mathematical Sciences Publishers, 2017-07-12)
Let $f$ be an $L^2$-normalized Hecke--Maass cuspidal newform of level $N$, character $\chi$ and Laplace eigenvalue $\lambda$. Let $N_1$ denote the smallest integer such that $N|N_1^2$ and $N_0$ denote the largest integer ...
Sup-norms of eigenfunctions in the level aspect for compact arithmetic surfaces
(Springer (part of Springer Nature), 2019-11-01)
Let $D$ be an indefinite quaternion division algebra over $\mathbb{Q}$. We approach the problem of bounding the sup-norms of automorphic forms $\phi$ on $D^\times(\mathbb{A})$ that belong to irreducible automorphic ...
The Manin constant and the modular degree
The Manin constant $c$ of an elliptic curve $E$ over $\mathbb{Q}$ is the nonzero integer that scales the pullback of a N\'{e}ron differential under a minimal parametrization $\phi\colon X_0(N)_{\mathbb{Q}} \twoheadrightarrow ...