Rong ChenAffiliation: Shanghai Normal University Title Of Talk: Congruence families for generalized Frobenius patitions
URLS: Abstract: Garvan, Sellers and Smoot discovered a remarkable symmetry in the families of congruences for generalized Frobenius partitions c\psi_{2,0} and c\psi_{2,1}. They also emphasized that the considerations for the general case of c\psi_{k,b} are important for future work. In the present work, we construct a vector-valued modular form for the generating functions of c\psi_{k,b}, and determine an equivalence relation among all b. Within each equivalence class, we can identify modular transformations relating the congruences of one c\psi_{k,b} to that of another c\psi_{k,b'}. Furthermore, correspondences between different equivalence classes can also be obtained through linear combinations of modular transformations. As an example, with the aid of these correspondences, we prove a family of congruences of c\phi_3, the Andrews' 3-colored Frobenius partition. This is a join work with Xiao-Jie Zhu.
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Last update made Tue Mar 10 21:28:02 CDT 2026.
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