Theta Constants, Riemann Surfaces and the Modular Group

By H. Farkas, I. Kra. 2001

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Modular A5 symmetry for flavour model building (2018, unknown): “) 3 ˝+ 8 10 ; ˝+ 1 5 ; 2;2(˝) 3 ˝+ 9 10 ; ˝+ 2 5 ; 2;3(˝) 3 ˝ 10 ; ˝+ 3 5 ; 2;4(˝) 3 ˝+ 1 10 ; ˝+ 4 5 : (2.15) 2For properties of these special functions, see, e.g., Refs. [37,38]. In the notations of Ref. [37], 3 0 0 . 4 S T T S S T T S T T T S T S T T T T 1,0 1,-1 1,2 1,1 1,3 1,4 2”
Topological Strings and (Almost) Modular Forms (2006, background): “Essential facts about them are reviewed in Appendix A; for a detailed study of modular forms of Γ(3), see [17].”
Generalised CP symmetry in modular-invariant models of flavour (2019, unknown): “ = q1=24 Y1 n=1 (1 qn) ; q= e2ˇi˝; (C.1) while the Jacobi 3 can be written as the series 3(z;˝) = X1 n=1 q~n2 e2ˇinz; q~= eˇi˝: (C.2) 14For the properties of this last special function, see, e.g. [49,50]. In the notations of Ref. [49], 3 0 0 . 30 N 2 ’S 3 3 ’A 4 4 ’S 4 5 ’A 5 Linear space dim.”