7 papers
Machine-Guided Recurrence Boundary Theory for Nahm Sums
Ankush Goswami
We develop a proof-carrying recurrence--boundary method for affine families of positive-definite Nahm sums. A universal coordinate-contiguous relation provides exact algebraic cell…
Sign Patterns in a Two Colored Partition Companion series
Aritram Dhar, Ankush Goswami, Mohit Tripathi
We study two closely related questions arising from the recent work of Andrews and El Bachraoui on the two-color partition series \[ S_1(q)=\sum_{n\ge0}s_1(n)q^n=\sum_{a\ge0}q^a(-q…
Separable integer partition classes and Slater's list -- II
Aritram Dhar, Ankush Goswami, Runqiao Li
Slater's list of Rogers-Ramanujan type identities remains a central source of striking series-product formulas in the theory of partitions and basic hypergeometric series. Although…
Weighted partitions with interval restrictions: exact formulas and a bivariate master identity
George E. Andrews, Mohamed El Bachraoui, Aritram Dhar +2
Let and be the signed partition functions introduced by Andrews and El Bachraoui for interval-restricted partitions whose parts greater than are controlle…
Separable integer partition classes and Slater's list -- I
Aritram Dhar, Ankush Goswami, Runqiao Li
Slater's list of Rogers-Ramanujan type identities consists of 130 series-product identities whose analytic proofs rely primarily on Bailey pair techniques. Although these identitie…
Resurgence, Habiro elements and strange identities
Samuel Crew, Veronica Fantini, Ankush Goswami +2
We prove resurgence properties for the Borel transform of a formal power series associated to elements in the Habiro ring that come from radial limits of partial theta series via s…