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The Arithmetic of Multiple Harmonic Sums.

dc.contributor.authorRosen, Julian H.en_US
dc.description.abstractThis dissertation concerns the arithmetic of a family of rational numbers called multiple harmonic sums. These sums are finite truncations of multiple zeta values. We consider multiple harmonic sums whose truncation point is one less than a prime. We derive families of congruences, involving multiple harmonic sums, for binomial coefficients and for values of the Kubota-Leopoldt p-adic L-function at positive integers. Congruences in our families hold modulo arbitrarily large powers of prime. We also set up a framework for studying congruences among multiple harmonic sums, which is related to a framework used in the study of multiple zeta values.en_US
dc.subjectMultiple Harmonic Sumsen_US
dc.titleThe Arithmetic of Multiple Harmonic Sums.en_US
dc.description.thesisdegreegrantorUniversity of Michigan, Horace H. Rackham School of Graduate Studiesen_US
dc.contributor.committeememberLagarias, Jeffrey C.en_US
dc.contributor.committeememberAdams, Fred C.en_US
dc.contributor.committeememberZieve, Michael E.en_US
dc.contributor.committeememberPrasanna, Kartiken_US
dc.contributor.committeememberSmith, Karen E.en_US
dc.owningcollnameDissertations and Theses (Ph.D. and Master's)

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