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math.NT2024
A segment of Euler product associated to a certain Dirichlet series
Rajat Gupta, Aditi Savalia
In the spirit of the work of Hardy-Littlewood and Lavrik, we study the Dirichlet series associated to the generalized divisor function . We obtain an exact i…
math.CO2024
Partitions in which every term but the smallest one is consecutive
Rajat Gupta, Noah Lebowitz-Lockard
In this article, we introduce the notion of almost consecutive partitions. A partition is almost consecutive if every term is consecutive, with the possible exception of the smalle…
math.NT2024
On the th smallest part of a partition into distinct parts
Rajat Gupta, Noah Lebowitz-Lockard, Joseph Vandehey
A classic theorem of Uchimura states that the difference between the sum of the smallest parts of the partitions of into an odd number of distinct parts and the corresponding s…