Geodesic
Sturm type theorem for Siegel modular forms of genus 2 modulo $p$
Dohoon Choi 1   ; YoungJu Choie 2   ; Toshiyuki Kikuta 3
1 School of Liberal Arts and Sciences Korea Aerospace University 200-1, Hwajeon-dong Goyang, Gyeonggi 412-791, Korea
2 Department of Mathematics Pohang University of Science and Technology Pohang, 790-784, Korea
3 Department of Mathematics Interdisciplinary Graduate School of Science and Engineering Kinki University Higashi-Osaka, 577-8502, Japan
Acta Arithmetica, Tome 158 (2013) no. 2, pp. 129-139 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa158-2-2
Mots-clés : suppose elliptic modular form integral coefficients sturm obtained bounds nonnegative integer every fourier coefficient vanishes modulo prime first fourier coefficients zero modulo present note study analogues sturms bounds siegel modular forms genus application study congruences involving analogue atkins operator fourier coefficients siegel modular forms genus

Dohoon Choi  1   ; YoungJu Choie  2   ; Toshiyuki Kikuta  3

1 School of Liberal Arts and Sciences Korea Aerospace University 200-1, Hwajeon-dong Goyang, Gyeonggi 412-791, Korea
2 Department of Mathematics Pohang University of Science and Technology Pohang, 790-784, Korea
3 Department of Mathematics Interdisciplinary Graduate School of Science and Engineering Kinki University Higashi-Osaka, 577-8502, Japan 
@article{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},
     pages = {129--139},
     year = {2013},
     volume = {158},
     number = {2},
     doi = {10.4064/aa158-2-2},
     language = {de},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa158-2-2/}
}
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 of genus 2 modulo $p$
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Dohoon Choi; YoungJu Choie; Toshiyuki Kikuta. Sturm type theorem for Siegel modular forms
 of genus 2 modulo $p$. Acta Arithmetica, Tome 158 (2013) no. 2, pp. 129-139. doi: 10.4064/aa158-2-2

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