A relation of modular discriminant Δ(τ)

Daeyeoul Kim
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 3, 1997, Number 4, Pages 181–184
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Daeyeoul Kim
Department of Mathematics.
Chonbuk National University,
Chonju. 5G1-75G Korea

Abstract

Let \Delta(\Lambda_{tau}) = \Delta(\tau} be modular discriminant and \Omega(\tau) = (2\pi)^4\eta(\tau)^8, where \eta(\tau) be Dedekind \eta-function.

(a) \Delta(\tau) = \pm \frac{1}{16}\Omega(\frac{\tau + 1}{2})\Omega(\frac{\tau}{2})( \overline{\rho}\Omega(\frac{\tau + 1}{2}) + \rho\Omega((\frac{\tau}{2})).

(b) \Delta(\tau) = \pm \left ( \frac{1}{16}\Omega(\frac{\tau + 1}{2})^2\Omega(\frac{\tau}{2})^2 - 16\frac{h_1 (\tau)^2}{ \Omega (\frac{\tau}{2}) \Omega(\frac{\tau + 1}{2})} \right ).

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Cite this paper

Kim, D. (1997). A relation of modular discriminant Δ(τ). Notes on Number Theory and Discrete Mathematics, 3(4), 181-184.

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