Beukers' modular form for zeta(3) irrationality is part of a one-parameter affine family for Gamma0(6)* that preserves the same exponential decay and denominator growth as Apery approximations.
Macdonald Symmetric functions and Hall polynomials
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Modular Forms and Numerical Explorations of Rational Approximations to $\zeta(3)$
Beukers' modular form for zeta(3) irrationality is part of a one-parameter affine family for Gamma0(6)* that preserves the same exponential decay and denominator growth as Apery approximations.