Another Family of q-Congruences Modulo the Square of a Cyclotomic Polynomial
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DOI: 10.1007/s00025-021-01423-4
Abstract: Using Bailey’s $$_{10}\phi _9$$ 10 ϕ 9 transformation formula, we prove a family of q -congruences modulo the square of a cyclotomic polynomial, which were previously observed by the author and Zudilin (J Math Anal… read more here.
Keywords: modulo square; cyclotomic polynomial; square cyclotomic; family congruences ... See more keywords
Congruences for overpartitions with restricted odd differences
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DOI: 10.1007/s13370-018-0624-y
Abstract: In recent work, Bringmann et al. used q-difference equations to compute a two-variable q-hypergeometric generating function for the number of overpartitions where (i) the difference between two successive parts may be odd only if the… read more here.
Keywords: congruences overpartitions; restricted odd; modulo overline; overpartitions restricted ... See more keywords
Congruences modulo powers of 5 for k -colored partitions
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DOI: 10.1016/j.jnt.2017.10.027
Abstract: Let $p_{-k}(n)$ enumerate the number of $k$-colored partitions of $n$. In this paper, we establish some infinite families of congruences modulo 25 for $k$-colored partitions. Furthermore, we prove some infinite families of Ramanujan-type congruences modulo… read more here.
Keywords: align; modulo powers; powers colored; colored partitions ... See more keywords
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
New infinite families of congruences for Andrews’ (K, I)-singular overpartitions
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DOI: 10.2989/16073606.2017.1419297
Abstract: Abstract In a recent work, Andrews defined the singular overpartition functions, denoted by , which count the number of overpartitions of n in which no part is divisible by k and only parts ≡ ±i… read more here.
Keywords: infinite families; families congruences; new infinite; congruences 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
Families of Ramanujan-Type Congruences Modulo 4 for the Number of Divisors
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DOI: 10.3390/axioms11070342
Abstract: In this paper, we explore Ramanujan-type congruences modulo 4 for the function σ0(n), counting the positive divisors of n. We consider relations of the form σ08(αn+β)+r≡0(mod4), with (α,β)∈N2 and r∈{1,3,5,7}. In this context, some conjectures… read more here.
Keywords: number divisors; type congruences; modulo number; families ramanujan ... See more keywords