Congruences modulo 8 for (2,k)-regular overpartitions for odd k>1

In this paper, we study various arithmetic properties of the function p ¯ 2 , k ( n ) , which denotes the number of ( 2 , k ) -regular overpartitions of n with odd k > 1 . We prove several infinite families of congruences modulo 8 for p ¯ 2 , k ( n ) . For example, we find that for all non-negati...

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Published inArabian Journal of Mathematics Vol. 7; no. 2; pp. 61 - 75
Main Authors Adiga, Chandrashekar, Naika, M. S. Mahadeva, Ranganatha, D., Shivashankar, C.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2018
Springer
Springer Nature B.V
Subjects
Congruences
Congruences (Mathematics)
Functions (Mathematics)
HyperText Markup Language
Integers
Mathematical research
Mathematics
Mathematics and Statistics
Partitions (Mathematics)
05A15
11P83
05A17
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ISSN2193-5343
2193-5351
2193-5351
DOI10.1007/s40065-017-0195-z

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Summary:In this paper, we study various arithmetic properties of the function p ¯ 2 , k ( n ) , which denotes the number of ( 2 , k ) -regular overpartitions of n with odd k > 1 . We prove several infinite families of congruences modulo 8 for p ¯ 2 , k ( n ) . For example, we find that for all non-negative integers β , n and k ≡ 1 ( mod 8 ) , p ¯ 2 , k ( 2 1 + β ( 16 n + 14 ) ) ≡ 0 ( mod 8 ) .
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ISSN:2193-5343
2193-5351
2193-5351
DOI:10.1007/s40065-017-0195-z