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

Eren Mehmet Kıral. "Bounds on sup-norms of half-integral weight modular forms." Acta Arithmetica 165.4 (2014): 385-399. <http://eudml.org/doc/279104>.

@article{ErenMehmetKıral2014,
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 $||y^\{κ/2\}f̃||_∞ ≪ _\{ε,κ\} N^\{1/2 - 1/18 +ε\}||y^\{κ/2\}f̃||_\{L^2\}$ for a modular form f̃ of level 4N and weight κ, a half-integer.},
author = {Eren Mehmet Kıral},
journal = {Acta Arithmetica},
keywords = {sup-norm; modular form; half-integral weight},
language = {eng},
number = {4},
pages = {385-399},
title = {Bounds on sup-norms of half-integral weight modular forms},
url = {http://eudml.org/doc/279104},
volume = {165},
year = {2014},
}

TY - JOUR
AU - Eren Mehmet Kıral
TI - Bounds on sup-norms of half-integral weight modular forms
JO - Acta Arithmetica
PY - 2014
VL - 165
IS - 4
SP - 385
EP - 399
AB - 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 $||y^{κ/2}f̃||_∞ ≪ _{ε,κ} N^{1/2 - 1/18 +ε}||y^{κ/2}f̃||_{L^2}$ for a modular form f̃ of level 4N and weight κ, a half-integer.
LA - eng
KW - sup-norm; modular form; half-integral weight
UR - http://eudml.org/doc/279104
ER -