Suppose that f is an elliptic modular form with integral coefficients. Sturm obtained bounds for a nonnegative integer n such that every Fourier coefficient of f vanishes modulo a prime p if the first n Fourier coefficients of f are zero modulo p. In the present note, we study analogues of Sturm's bounds for Siegel modular forms of genus 2. As an application, we study congruences involving an analogue of Atkin's U(p)-operator for the Fourier coefficients of Siegel modular forms of genus 2.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa158-2-2,
author = {Dohoon Choi and YoungJu Choie and Toshiyuki Kikuta},
title = {Sturm type theorem for Siegel modular forms of genus 2 modulo p},
journal = {Acta Arithmetica},
volume = {161},
year = {2013},
pages = {129-139},
zbl = {1288.11046},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa158-2-2}
}
Dohoon Choi; YoungJu Choie; Toshiyuki Kikuta. Sturm type theorem for Siegel modular forms of genus 2 modulo p. Acta Arithmetica, Tome 161 (2013) pp. 129-139. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa158-2-2/