Zobrazeno 1 - 10
of 671
pro vyhledávání: '"11P83"'
In 2014, as part of a larger study of overpartitions with restrictions of the overlined parts based on residue classes, Munagi and Sellers defined $d_2(n)$ as the number of overpartitions of weight $n$ wherein only even parts can be overlined. As par
Externí odkaz:
http://arxiv.org/abs/2411.03077
A partition is said to be $\ell$-regular if none of its parts is a multiple of $\ell$. Let $b^\prime_5(n)$ denote the number of 5-regular partitions into distinct parts (equivalently, into odd parts) of $n$. This function has also close connections t
Externí odkaz:
http://arxiv.org/abs/2411.02978
Autor:
Saikia, Manjil P., Sarma, Abhishek
In this short note, we prove several new congruences for the overcubic partition triples function, using both elementary techniques and the theory of modular forms. These extend the recent list of such congruences given by Nayaka, Dharmendra, and Kum
Externí odkaz:
http://arxiv.org/abs/2411.00013
The Fourier coefficients $c_1(n)$ of the elliptic modular $j$-function are always even for $n \not\equiv 7 \pmod{8}$. In contrast, for $n \equiv 7 \pmod{8}$, it is conjectured that ``half" of the coefficients take odd values. In this article, we firs
Externí odkaz:
http://arxiv.org/abs/2410.06745
This paper is devoted to the study of $$ U_t(a,q):=\sum_{1\leq n_1
Externí odkaz:
http://arxiv.org/abs/2409.20400
Autor:
Sellers, James A.
In a recent article on overpartitions, Merca considered the auxiliary function $a(n)$ which counts the number of partitions of $n$ where odd parts are repeated at most twice (and there are no restrictions on the even parts). In the course of his work
Externí odkaz:
http://arxiv.org/abs/2409.12321
Publikováno v:
Journal of Integer Sequences 27 (2024), Article 24.4.5
Recently, Gireesh, Ray, and Shivashankar studied an analog, $\overline{a}_t(n)$, of the $t$-core partition function, $c_t(n)$. In this paper, we study the function $\overline{a}_5(n)$ in conjunction with $c_5(n)$ as well as another analogous function
Externí odkaz:
http://arxiv.org/abs/2409.02034
Publikováno v:
Integers 23 (2023), A40
Recently, Jha (arXiv:2007.04243, arXiv:2011.11038) has found identities that connect certain sums over the divisors of $n$ to the number of representations of $n$ as a sum of squares and triangular numbers. In this note, we state a generalized result
Externí odkaz:
http://arxiv.org/abs/2409.02023
Publikováno v:
Integers 21 (2021), A83
Recently, Merca and Schmidt found some decompositions for the partition function $p(n)$ in terms of the classical M\"{o}bius function as well as Euler's totient. In this paper, we define a counting function $T_k^r(m)$ on the set of $n$-color partitio
Externí odkaz:
http://arxiv.org/abs/2409.02004
Autor:
Zudilin, Wadim
Given a newform with the Fourier expansion $\sum_{n=1}^\infty b(n)q^n\in\mathbb Z[[q]]$, a prime $p$ is said to be non-ordinary if $p\mid b(p)$. We exemplify several newforms of weight 4 for which the latter divisibility implies a stronger divisibili
Externí odkaz:
http://arxiv.org/abs/2409.00384