Let G be the group of the fractional linear transformations generated by T（τ）=τ ＋ λ, S（τ）=（τ cos π/n ＋ sin π/n）/（-τ sin π/n ＋ cos π/n）;where λ=2（cos π/m ＋ cos π/n）/sin π/n;m, n is a pair of...Let G be the group of the fractional linear transformations generated by T（τ）=τ ＋ λ, S（τ）=（τ cos π/n ＋ sin π/n）/（-τ sin π/n ＋ cos π/n）;where λ=2（cos π/m ＋ cos π/n）/sin π/n;m, n is a pair of integers with either n ≥ 2, m ≥ 3 or n ≥ 3, m ≥ 2; τ lies in the upper half plane H.A fundamental set of functions f0, fi and f∞ automorphic with respect to G will be constructed from the conformal mapping of the fundamental domain of G. We derive an analogue of Ramanujan＇s triple differential equations associated with the group G and establish the connection of f0, fi and f∞ with a family of hypergeometric functions.展开更多
文摘Let G be the group of the fractional linear transformations generated by T（τ）=τ ＋ λ, S（τ）=（τ cos π/n ＋ sin π/n）/（-τ sin π/n ＋ cos π/n）;where λ=2（cos π/m ＋ cos π/n）/sin π/n;m, n is a pair of integers with either n ≥ 2, m ≥ 3 or n ≥ 3, m ≥ 2; τ lies in the upper half plane H.A fundamental set of functions f0, fi and f∞ automorphic with respect to G will be constructed from the conformal mapping of the fundamental domain of G. We derive an analogue of Ramanujan＇s triple differential equations associated with the group G and establish the connection of f0, fi and f∞ with a family of hypergeometric functions.
