Hausdorff and packing dimensions of non-normal tuples of numbers: Non-linearity and divergence points

AbstractWe apply the results in [L. Olsen, Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averages, J. Math. Pures Appl. 82 (2003) 1591–1649; L. Olsen, Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averages. III, Aequationes Math. 71 (2006) 29–53; L. Olsen, Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averages. IV: Divergence points and packing dimension, Bull. Sci. Math. 132 (2008) 650–678; L. Olsen, S. Winter, Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averages. II: Non-linearity, divergence points and Banach space valued spectra, Bull. Sci. Math. 131 (2007) 518–558] to give a systematic and detailed account of the Hausdorff and packing dimensions of sets of d-tuples of numbers defined in terms of the asymptotic behaviour of the frequencies of strings of digits in their N-adic expansion