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Sums of Reciprocals of Fractional Parts and Multiplicative Diophantine Approximation (Memoirs of the American Mathematical Society, January 2020, 263-1276)
1470440954 pdf After after setting out problems and main results for sums of reciprocals of fractional parts and multiplicative diophantine approximations, Beresnevich, Haynes, and Velani develop techniques and establish the main results. They cover Ostrowski expansion, a gaps lemma and its consequences, establishing the homogeneous results on sums of reciprocals, establishing the inhomogeneous results on sums of reciptocals, and proofs of the four main theorems. Annotation 2020 Ringgold, Inc., Portland, OR (protoview.com)