標題: Defining equations of modular curves
作者: Yang, Yifan
應用數學系
Department of Applied Mathematics
關鍵字: modular curves;generalized Dedekind eta-functions;cusp forms;modular parameterization of rational elliptic curves
公開日期: 20-Aug-2006
摘要: We obtain defining equations of modular curves X-0(N), X-1(N), and X(N) by explicitly constructing modular functions using generalized Dedekind eta functions. As applications, we describe a method of obtaining a basis for the space of cusp forms of weight 2 on a congruence subgroup. We also use our model of X-0(37) to find explicit modular parameterization of rational elliptic curves of conductor 37. (C) 2005 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.aim.2005.05.019
http://hdl.handle.net/11536/11910
ISSN: 0001-8708
DOI: 10.1016/j.aim.2005.05.019
期刊: ADVANCES IN MATHEMATICS
Volume: 204
Issue: 2
起始頁: 481
結束頁: 508
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