Showing math.NTShow all
3 papers · 1 filter
math.NT2025
Certain positive -series and inequalities for two-color partitions
George E. Andrews, Mohamed El Bachraoui
We consider some -series which depend on a pair of positive integers . While positivity of these series holds for the first few values of , the situation is quite…
math.NT2025
Positive Weighted Partitions Generated by Double Series
George E. Andrews, Mohamed El Bachraoui
We investigate some weighted integer partitions whose generating functions are double-series. We will establish closed formulas for these -double series and deduce that their co…
math.NT2024
Legendre theorems for certain overpartitions and overpartition pairs
George E. Andrews, Mohamed El Bachraoui
Motivated by two Legendre-type formulas for overpartitions, we derive a variety of their companions as Legendre theorems for overpartition pairs. This leads to equalities of subcla…