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ON ANDREWS’ PARTITION FUNCTION EO(n)
Fathima S. N.,Veena V. S. 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.3
Recently, Andrews introduced partition functions EO(n) and EO(n) where the function EO(n) denotes the number of partitions of n in which every even part is less than each odd part and the function EO(n) denotes the number of partitions enumerated by EO(n) in which only the largest even part appears an odd number of times. In this paper, we prove new congruences for EO(n) and pD(n), the number of partitions into distinct (or, odd) parts. We further establish linear recurrence relations for pD(n), which counts the number of partitions of n into distinct parts with 2 types of each part and EO(n).
5 REGULAR PARTITIONS WITH DISTINCT ODD PARTS
VEENA V. S.,FATHIMA S. N. 장전수학회 2021 Advanced Studies in Contemporary Mathematics Vol.31 No.2
In this article, we prove infinite families of congruences for pod5(n) (the number of 5-regular partitions of n with distinct odd parts (and even parts are unrestricted)) using the theory of Hecke eigenforms. We also study the divisibility properties of pod5(n) using the arithmetic properties of modular forms.
Divisibility and arithmetic properties of certain $\ell$-regular overpartition pairs
Anusree Anand,S.N. Fathima,M.A. Sriraj,P. Siva Kota Reddy 한국전산응용수학회 2024 Journal of applied mathematics & informatics Vol.42 No.4
For an integer $\ell \geq1$, let ${\bar{B}_{\ell}}(n)$ denotes the number of $\ell $-regular over partition pairs of $n$. For certain conditions of $\ell$, we study the divisibility of ${\bar{B}_{\ell}}(n)$ and arithmetic properties for ${\bar{B}_{\ell}}(n)$. We further obtain infinite family of congruences modulo $2^t$ satisfied by $\bar{B}_{3}(n)$ employing a result of Ono and Taguchi (2005) on nilpotency of Hecke operators.
ON SOME CIRCULAR SUMMATION FORMULAS FOR THETA FUNCTIONS
YUDHISTHIRA JAMUDULIA,S. N. FATHIMA 장전수학회 2017 Proceedings of the Jangjeon mathematical society Vol.20 No.1
In his lost notebook, Ramanujan claimed that the "circular" summation of nth power of his symmetric theta function f(a, b) satisfies a factorization of the form f(a, b)F(ab). In this paper, we obtain new circular summation formula of theta functions using the theory of elliptic functions. As an application, we also obtain few interesting identity of the theta functions.
Six-variable generalization of reciprocity theorem found in Ramanujan's lost notebook
YUDHISTHIRA JAMUDULIA,S. N. FATHIMA 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.4
In this paper, we derive a six variable generalization of Jacobi triple product from three variable reciprocity theorem by parameter augmentation. Further we derive some q-gamma, q-beta and eta-function identities from this identity.
Some congruence properties for -regular partitions, where l ∈ {4, 8, 13, 17, 19, 25, 40, 55}
P. Murugan,V. S. Veena,S. N. Fathima 장전수학회 2023 Proceedings of the Jangjeon mathematical society Vol.26 No.2
Some congruence properties for -regular partitions, where l ∈ {4, 8, 13, 17, 19, 25, 40, 55}