Quantum infinitesimal Weierstrass equation conjecture

Let μ,θnc{}^{\bullet}\wp^{\mathrm{nc}}_{\mu,\theta} and μ,θ{}^{\bullet}\wp'_{\mu,\theta} be the quantum nonstandard Weierstrass function and its derivative, and let E(μ,θ)quant(X,Y){}^{\bullet}\mathrm{E}^{\mathrm{quant}}_{(\mu,\theta)}(X,Y) denote the corresponding quantum infinitesimal Weierstrass equation. The relation \simeq_{\ast} denotes the relevant infinitesimal equivalence. Quantum Weierstrass conjecture. The pair (μ,θnc,μ,θ)({}^{\bullet}\wp^{\mathrm{nc}}_{\mu,\theta},{}^{\bullet}\wp'_{\mu,\theta}) is a solution of

E(μ,θ)quant(X,Y)0.{}^{\bullet}\mathrm{E}^{\mathrm{quant}}_{(\mu,\theta)}(X,Y)\simeq_{\ast}0.

The preceding discussion shows only that the equation is satisfied trivially with respect to the weaker relation \simeq; the conjecture asks for the stronger infinitesimal relation \simeq_{\ast}, which is not established in the supplied text.

Sources & referencesView supporting material

Primary source

C. Castaño Bernard and T. M. Gendron, “Modular Invariant of Quantum Tori”, arXiv:0909.0143 (2013).

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