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Sept. 2001 On $d$-gonality of Drinfel'd modular curves and strong Uniform Boundedness Conjecture
Viet NguyenKhac, Shin-ichiro Yamada
Proc. Japan Acad. Ser. A Math. Sci. 77(7): 126-129 (Sept. 2001). DOI: 10.3792/pjaa.77.126

Abstract

We give an upper bound of the level $\mathfrak{n}$ by means of $d$-gonality of the Drinfel'd modular curves $X_0(\mathfrak{n})$ mod $\mathfrak{p}$ for $\mathfrak{p} \nmid \mathfrak{n}$. As a corollary of the result, we obtain an estimation in the strong Uniform Boundedness Conjecture for Drinfel'd modules of rank 2. We also discuss some asymptotically (and practically) good bound in this connection.

Citation

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Viet NguyenKhac. Shin-ichiro Yamada. "On $d$-gonality of Drinfel'd modular curves and strong Uniform Boundedness Conjecture." Proc. Japan Acad. Ser. A Math. Sci. 77 (7) 126 - 129, Sept. 2001. https://doi.org/10.3792/pjaa.77.126

Information

Published: Sept. 2001
First available in Project Euclid: 23 May 2006

MathSciNet: MR1857289
Digital Object Identifier: 10.3792/pjaa.77.126

Subjects:
Primary: 11G09 , 11G30 , 14H10

Keywords: $d$-gonality , bounding torsions , Drinfel'd modular curve , strong uniform boundedness conjecture

Rights: Copyright © 2001 The Japan Academy

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Vol.77 • No. 7 • Sept. 2001
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