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Modular equations for congruence subgroups of genus zero (II)open access
- Authors
- Cho, Bumkyu
- Issue Date
- Feb-2022
- Publisher
- Elsevier Inc.
- Keywords
- Modular equations; Modular polynomials; Kronecker's congruence relation
- Citation
- Journal of Number Theory, v.231, pp 48 - 79
- Pages
- 32
- Indexed
- SCIE
SCOPUS
- Journal Title
- Journal of Number Theory
- Volume
- 231
- Start Page
- 48
- End Page
- 79
- ISSN
- 0022-314X
1096-1658
- Abstract
- We present a result that the modular equation of a Haupt-modul for a certain congruence subgroup Gamma(H) (N, t) of genus zero satisfies Kronecker's congruence relation. This generalizes the author's previous result about Gamma(1) (m) boolean AND Gamma(0) (MN). Furthermore we show that the similar result holds for a certain congruence subgroup F of genus zero with [Gamma : Gamma(H) (N, t)] = 2. Finally we prove a conjecture of Lee and Park, asserting that the modular equation of the continued fraction of order six satisfies a certain form of Kronecker's congruence relation. (C) 2020 Elsevier Inc. All rights reserved.
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Related Researcher
- Cho, Bum Kyu
- College of Natural Science (Department of Mathematics)