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pro vyhledávání: '"CRAIG, William"'
Andrews-Dyson-Hickerson, Cohen build a striking relation between q-hypergeometric series, real quadratic fields, and Maass forms. Thanks to the works of Lewis-Zagier and Zwegers we have a complete understanding on the part of these relations pertaini
Externí odkaz:
http://arxiv.org/abs/2409.17818
Autor:
Craig, William
In recent years, the generalized sum-of-divisor functions of MacMahon have been unified into the algebraic framework of $q$-multiple zeta values. In particular, these results link partition theory, quasimodular forms, $q$-multiple zeta values, and qu
Externí odkaz:
http://arxiv.org/abs/2409.13874
We study zero attractors for polynomials built from partition statistics, complementing earlier work in this direction by Boyer, Goh, Parry, and others. In particular, using analytic methods we establish the zero attractor of partition $t$-hook polyn
Externí odkaz:
http://arxiv.org/abs/2408.16902
We confirm the speculation that the distribution of $t$-hooks among unrestricted integer partitions essentially descends to self-conjugate partitions. Namely, we prove that the number of hooks of length $t$ among the size $n$ self-conjugate partition
Externí odkaz:
http://arxiv.org/abs/2406.09059
We show that integer partitions, the fundamental building blocks in additive number theory, detect prime numbers in an unexpected way. Answering a question of Schneider, we show that the primes are the solutions to special equations in partition func
Externí odkaz:
http://arxiv.org/abs/2405.06451
The study of partitions with parts separated by parity was initiated by Andrews in connection with Ramanujan's mock theta functions, and his variations on this theme have produced generating functions with a large variety of different modular propert
Externí odkaz:
http://arxiv.org/abs/2403.00635
Recently, MacMahon's generalized sum-of-divisor functions were shown to link partitions, quasimodular forms, and q-multiple zeta values. In this paper, we explore many further properties and extensions of these. Firstly, we address a question of Ono
Externí odkaz:
http://arxiv.org/abs/2402.08340