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

Eren Mehmet Kıral

Acta Arithmetica, Tome 166 (2014), p. 385-399 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $| | y^{κ / 2} {f ̃ | |}_{\infty} ≪_{ε, κ} N^{1 / 2 - 1 / 18 + ε} | | y^{κ / 2} f ̃ {| |}_{L^{2}}$ for a modular form f̃ of level 4N and weight κ, a half-integer.

Publié le : 2014-01-01

Zbl 1329.11032

EUDML-ID : urn:eudml:doc:279104

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     author = {Eren Mehmet K\i ral},
     title = {Bounds on sup-norms of half-integral weight modular forms},
     journal = {Acta Arithmetica},
     volume = {166},
     year = {2014},
     pages = {385-399},
     zbl = {1329.11032},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa165-4-7}
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Eren Mehmet Kıral. Bounds on sup-norms of half-integral weight modular forms. Acta Arithmetica, Tome 166 (2014) pp. 385-399. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa165-4-7/