Alexandru Ciolan

activity

20172021

most citedRanks of overpartitions: Asymptotics and inequalities

12 citations · 30 across the 4 of their papers we have counts for

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6 papers · 1 filter

math.NT2021★ 8 cited

Landau and Ramanujan approximations for divisor sums and coefficients of cusp forms

Alexandru Ciolan, Alessandro Languasco, Pieter Moree

In 1961, Rankin determined the asymptotic behavior of the number $S_{k, q} (x)$ of positive integers $n \leq x$ for which a given prime $q$ does not divide $σ_{k} (n),$ the $k$ -th divisor…

math.NT2020

Inequalities between overpartition ranks for all moduli

Alexandru Ciolan

In this paper we give a full description of the inequalities that can occur between overpartition ranks. If $N (a, c, n)$ denotes the number of overpartitions of $n$ wi…

math.NT2020★ 3 cited

Equidistribution and inequalities for partitions into powers

Alexandru Ciolan

If $p_{k} (a, m, n)$ denotes the number of partitions of $n$ into $k$ th powers with a number of parts that is congruent to $a$ modulo $m,$ then $p_{2} (0, 2, n) \sim p_{2} (1, 2, n)$ and the s…

math.NT2019★ 12 cited

Ranks of overpartitions: Asymptotics and inequalities

Alexandru Ciolan

In this paper we compute asymptotics for the coefficients of an infinite class of overpartition rank generating functions. Using these results, we show that $ \overline{N}(a,c,n),…

math.NT2018★ 7 cited

Asymptotics and inequalities for partitions into squares

Alexandru Ciolan

In this paper we prove that the number of partitions into squares with an even number of parts is asymptotically equal to that of partitions into squares with an odd number of part…

math.NT2017

Browkin's discriminator conjecture

Alexandru Ciolan, Pieter Moree

Let $q \geq 5$ be a prime and put $q^{*} = (- 1)^{(q - 1) /2} \cdot q$ . We consider the integer sequence $u_{q} (1), u_{q} (2), \dots,$ with $u_{q} (j) = (3^{j} - q^{*} (- 1)^{j}) /4$ . No term in this sequence is r…