Overpartition function modulo powers of 2

Let p ¯ ( n ) denote the number of overpartitions of n . Recently, congruences modulo powers of 2 for p ¯ ( n ) were widely studied. In this paper, we prove several new infinite families of congruences modulo powers of 2 for p ¯ ( n ) . For example, for α ≥ 1 and n ≥ 0 , p ¯ ( 8 · 3 4 α + 4 n + 5 ·...

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Bibliographic Details
Published in:The Ramanujan journal 2017-10, Vol.44 (1), p.89-104
Main Authors: Yang, Xue, Cui, Su-Ping, Lin, Bernard L. S.
Format: Article
Language:English
Subjects:
Combinatorics
Congruences
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
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Summary:Let p ¯ ( n ) denote the number of overpartitions of n . Recently, congruences modulo powers of 2 for p ¯ ( n ) were widely studied. In this paper, we prove several new infinite families of congruences modulo powers of 2 for p ¯ ( n ) . For example, for α ≥ 1 and n ≥ 0 , p ¯ ( 8 · 3 4 α + 4 n + 5 · 3 4 α + 3 ) ≡ 0 ( mod 2 8 ) .
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-016-9784-2