A new higher-dimensional irrationality criterion for periods expressed as Mellin integrals, based on upper bounds for multivariate transfinite diameters, is applied to give an alternative proof of the irrationality of zeta(2).
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Multivariable Vandermonde determinants are rewritten as sums of completely factorizing Vandermonde determinants in fewer variables via amalgamated matrix determinant formulae derived from Specht module theory, yielding an elementary proof of transfinite diameter multiplicativity.
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Mellin transforms, transfinite diameter and rational approximations of integrals
A new higher-dimensional irrationality criterion for periods expressed as Mellin integrals, based on upper bounds for multivariate transfinite diameters, is applied to give an alternative proof of the irrationality of zeta(2).
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Multivariable Vandermonde determinants, amalgams of matrices and Specht modules
Multivariable Vandermonde determinants are rewritten as sums of completely factorizing Vandermonde determinants in fewer variables via amalgamated matrix determinant formulae derived from Specht module theory, yielding an elementary proof of transfinite diameter multiplicativity.