Geometric deduction of the solutions to modular equations
Geometric deduction of the solutions to modular equations
复制标题
模方程解的几何推导
DOI：
10.1007/s11139-022-00604-1
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Sugawa Toshiyuki
中科院分区：
文献类型：
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作者：
Alam Md. Shafiul;Sugawa Toshiyuki
在他的笔记中，拉马努金在没有证明的情况下提出了许多关于广义模方程解的重要公式。很久以后，利用级数和超几何函数的高度非平凡恒等式提供了这个公式的证明。我们提供了一种几何方法来证明这些公式。我们强调，我们的证明是几何的，与这些恒等式无关。
In his notebooks, Ramanujan presented without proof many remarkable formulae for the solutions to generalized modular equations. Much later, proofs of the formulae were provided by making use of highly nontrivial identities for theta series and hypergeometric functions. We offer a geometric approach to the proof of those formulae. We emphasize that our proofs are geometric and independent of such identities.