L^\infty norms of holomorphic modular forms in the case of compact quotient

Soumya Das; Jyoti Sengupta

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arXiv · 1301.3677

L^\infty norms of holomorphic modular forms in the case of compact quotient

Soumya Das·Jyoti Sengupta

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Abstract

We prove a sub-convex estimate for the sup-norm of $L^2$-normalized holomorphic modular forms of weight $k$ on the upper half plane, with respect to the unit group of a quaternion division algebra over $\mf Q$. More precisely we show that when the $L^2$ norm of an eigenfunction $f$ is one, | f |_\infty \ll k^{1/2 - 12/131 + \varepsilon}, for any $\varepsilon>0$ and for all $k$ sufficiently large.

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Soumya Das, Jyoti Sengupta. 2013-01-16. L^\infty norms of holomorphic modular forms in the case of compact quotient. https://arxiv.org/abs/1301.3677

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