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Математические заметки, 2020, том 107, выпуск 3, статья опубликована в англоязычной версии журнала
(Mi mzm12773)
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Эта публикация цитируется в 5 научных статьях (всего в 5 статьях)
Статьи, опубликованные в английской версии журнала
Some Congruences for Overpartitions with Restriction
H. M. Srivastavaabc, N. Saikiad a Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, V8W 3R4, Canada
b Department of Medical Research, China Medical University, Taichung,
Taiwan, 40402, Republic of China
c Department of Mathematics and Informatics, Azerbaijan University,
Baku, AZ1007, Azerbaijan
d Department of Mathematics, Rajiv Gandhi University, Doimukh,
Arunachal Pradesh, 791112, India
Аннотация:
For any given positive integers
$m$
and
$n$,
let
$\overline{p}_m(n)$
denote the number of overpartitions of
$n$
with no parts divisible by
$4m$
and only the parts congruent to
$m$
modulo
$2m$
overlined.
In this paper, we prove Ramanujan-type congruences modulo 2 for
$\overline{p}_m(n)$
by applying
$q$-series and Ramanujan's theta-function identities.
Ключевые слова:
congruences, partitions,
generating functions, overpartitions with restriction,
theta-function identities.
Поступило: 02.12.2019
Образец цитирования:
H. M. Srivastava, N. Saikia, “Some Congruences for Overpartitions with Restriction”, Math. Notes, 107:3 (2020), 488–498
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/mzm12773
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