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Bounds on sup-norms of half-integral weight modular forms

Volume 165 / 2014

Eren Mehmet Kıral Acta Arithmetica 165 (2014), 385-399 MSC: Primary 11F03; Secondary 11F37. DOI: 10.4064/aa165-4-7

Abstract

Bounding sup-norms of modular forms in terms of the level has been the focus of much recent study. In this work the sup-norm of a half-integral weight cusp form is bounded in terms of the level: we prove that $\|y^{\kappa/2}\tilde{f}\|_\infty \ll_{\varepsilon,\kappa} N^{1/2 - 1/18 +\varepsilon}\|y^{\kappa/2}\tilde{f}\|_{L^2}$ for a modular form $\tilde{f}$ of level $4N$ and weight $\kappa$, a half-integer.

Authors

  • Eren Mehmet KıralBrown University
    151 Thayer Street
    Providence, RI 02912, U.S.A.
    e-mail

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