Additive Number Theory and Partitions - Brossura

Pierantozzi ScD, Donald C

9781688372771: Additive Number Theory and Partitions

Brossura

ISBN 10: 1688372776 ISBN 13: 9781688372771

Casa editrice: Independently published, 2019

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It is well known that partitions and their associated Ferrers-Young diagrams and tableaux play an important role in the study of hypergeometric functions, combinatorics, representation theory, Lie algebras, and statistical mechanics. In some cases the combinatorial properties of the partitions and Ferrers-Young diagrams are important, while in others the content of the theorems rely on identities involving relevant q-series generating functions. In this investigation we show that the values of the partition function p(n), viewed as q-coefficients, play a key role in the arithmetic of several infinite families of modular L-functions. In particular, this suggests that there is a ‘correspondence’ between Tate-Shafarevich groups of certain motives of modular forms and sets of partitions.Initial studies into the development of partitions was undertaken by Srinivasa Ramanujan. Subsequently, the work was greatly extended and intimately adapted to modular forms central to the solution of Fermat’s Last Theorem by Hans Rademacher while at the University of Pennsylvania.Herein this work is studied and examined along with its extended application to modular forms through Farey sequences and the Ford circle method.

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