The paper claims that the mass matrices of leptons, quarks, and neutrinos are Fourier coefficient matrices of SL(2,Z(√2)) modular forms, with parameter-free agreement for charged leptons and fitted agreement for quarks and neutrinos.
The usual treatment of these variables is to regard them as a scalar field in the four-dimensional space-time and to try t o find a way to stabilize them
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The paper claims that the mass matrices of leptons, quarks, and neutrinos are Fourier coefficient matrices of SL(2,Z(√2)) modular forms, with parameter-free agreement for charged leptons and fitted agreement for quarks and neutrinos.