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Let $kappa$ be a positive real number and $minmathbb{N}cup{infty}$ be given. Let $p_{kappa, m}(n)$ denote the number of partitions of $n$ into the parts from the Piatestki-Shapiro sequence $(lfloor ell^{kappa}rfloor)_{ellin mathbb{N}}$ with at most $m$ times (repetition allowed). In this paper we establish asymptotic formulas of Hardy-Ramanujan type for $p_{kappa, m}(n)$, by employing a framework of asymptotics of partitions established by Roth-Szekeres in 1953, as well as some results on equidistribution.
In recent work, M. Schneider and the first author studied a curious class of integer partitions called sequentially congruent partitions: the $m$th part is congruent to the $(m+1)$th part modulo $m$, with the smallest part congruent to zero modulo th
In this paper, we reprove a global converse theorem of Cogdell and Piatetski-Shapiro using purely global methods.
Integer partitions express the different ways that a positive integer may be written as a sum of other positive integers. Here we explore the analytic properties of a polynomial $f_lambda(x)$ that we call the partition polynomial for the partition $l
We study a curious class of partitions, the parts of which obey an exceedingly strict congruence condition we refer to as sequential congruence: the $m$th part is congruent to the $(m+1)$th part modulo $m$, with the smallest part congruent to zero mo
Partitions, the partition function $p(n)$, and the hook lengths of their Ferrers-Young diagrams are important objects in combinatorics, number theory and representation theory. For positive integers $n$ and $t$, we study $p_t^e(n)$ (resp. $p_t^o(n)$)