George E. Andrews

Affiliation: The Pennsylvania State University

Title Of Talk: Partition problems in the spirit of MacMahon

Abstract: (The talk is joint work with T. Amdeberhan, M. Merca, S. Rose and R. Tauraso). In the paper, Further Study on MacMahon-Type Sums of Divisors (Res. in Number Th.11, \#19, (2025)), Amdeberhan, Tauraso and I studied five new generating functions (parametrized by an index a taking the values $-2,-1,0,1,2$) generalizing the functions studied by P.A. MacMahon in his paper, Divisors of Numbers and Their Continuations in the Theory of Partitions (Proc. London Math. Soc. (2), 19(1920), 305-340). In this talk, we concentrate on the a=0 case where a new representation of the generating function has close connections with polynomials whose roots provide the maximal real subfields of the cyclotomic fields. We shall also discuss open problems.

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