Arithmetic Properties of 9-Regular Partitions with Distinct Odd Parts
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DOI: 10.1007/s40306-018-0274-z
Abstract: AbstractLet pod9(n)$\text {pod}_{9}(n)$, ped9(n)$\text {ped}_{9}(n)$, and A¯9(n)$\overline {A}_{9}(n)$ denote the number of 9-regular partitions of n wherein odd parts are distinct, even parts are distinct, and the number of 9-regular overpartitions of n, respectively. By… read more here.
Keywords: regular partitions; arithmetic properties; text pod; properties regular ... See more keywords
Arithmetic properties of the sum of divisors
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DOI: 10.1016/j.jnt.2020.11.014
Abstract: The divisor function $\sigma(n)$ denotes the sum of the divisors of the positive integer $n$. For a prime $p$ and $m \in \mathbb{N}$, the $p$-adic valuation of $m$ is the highest power of $p$ which… read more here.
Keywords: arithmetic properties; properties sum; sum divisors;
ARITHMETIC PROPERTIES OF COEFFICIENTS OF THE MOCK THETA FUNCTION $B(q)$
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DOI: 10.1017/s0004972719001175
Abstract: We investigate the arithmetic properties of the second-order mock theta function $B(q)$ and establish two identities for the coefficients of this function along arithmetic progressions. As applications, we prove several congruences for these coefficients. read more here.
Keywords: properties coefficients; theta function; mock theta; coefficients mock ... See more keywords
ARITHMETIC PROPERTIES OF 3-REGULAR PARTITIONS IN THREE COLOURS
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DOI: 10.1017/s0004972721000411
Abstract: Abstract Gireesh and Mahadeva Naika [‘On 3-regular partitions in 3-colors’, Indian J. Pure Appl. Math. 50 (2019), 137–148] proved an infinite family of congruences modulo powers of 3 for the function $p_{\{3,3\}}(n)$ , the number… read more here.
Keywords: properties regular; regular partitions; arithmetic properties; three colours ... See more keywords
On New Arithmetic Properties of Determinants of Hankel Matrices
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DOI: 10.1134/s1064562418050216
Abstract: We construct an infinite-dimensional Hankel matrix H∞ with elements of the form m/2l, where m, l ∈ ℤ, with the following property: the divisors of the numerators of its principal minors contain all prime numbers. read more here.
Keywords: arithmetic properties; new arithmetic; properties determinants; hankel matrices ... See more keywords
Arithmetic properties of 5-regular bipartitions
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DOI: 10.1142/s179304211750049x
Abstract: Let Bt(n) denote the number of t-regular bipartitions of n. In this work, we establish several infinite families of congruences modulo powers of 2 and 5 for B5(n). For example, we find that for all… read more here.
Keywords: regular bipartitions; properties regular; arithmetic properties;
Arithmetic properties for Andrews’ (48,6)- and (48,18)-singular overpartitions
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DOI: 10.1515/math-2019-0026
Abstract: Abstract Singular overpartition functions were defined by Andrews. Let Ck,i(n) denote the number of (k, i)-singular overpartitions of n, which counts the number of overpartitions of n in which no part is divisible by k… read more here.
Keywords: arithmetic properties; andrews singular; number; properties andrews ... See more keywords
Arithmetic properties for two restricted partitions modulo powers of 5
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DOI: 10.2989/16073606.2018.1544945
Abstract: Abstract Let pk,3(n) count the number of 2-color partition triples of n where one of the colors appears only in parts that are multiples of k and Bk,ℓ(n) denote the number of (k, ℓ)-regular bipartitions… read more here.
Keywords: infinite families; arithmetic properties; families congruences; modulo powers ... See more keywords