Bibliographic Details
| Title: |
On some new arithmetic properties of certain restricted color partition functions. |
| Authors: |
Dasappa, Ranganatha1 (AUTHOR) ddranganatha@gmail.com, Channabasavayya1 (AUTHOR), Keerthana, Gedela Kavya1 (AUTHOR) |
| Source: |
Arabian Journal of Mathematics. Aug2024, Vol. 13 Issue 2, p275-289. 15p. |
| Subject Terms: |
*PARTITION functions, *ARITHMETIC, *MATHEMATICS, *GEOMETRIC congruences, *COLOR, *WITNESSES, *EISENSTEIN series |
| Abstract: |
Very recently, Pushpa and Vasuki (Arab. J. Math. 11, 355–378, 2022) have proved Eisenstein series identities of level 5 of weight 2 due to Ramanujan and some new Eisenstein identities for level 7 by the elementary way. In their paper, they introduced seven restricted color partition functions, namely P ∗ (n) , M (n) , T ∗ (n) , L (n) , K (n) , A (n) , and B(n), and proved a few congruence properties of these functions. The main aim of this paper is to obtain several new infinite families of congruences modulo 2 a · 5 ℓ for P ∗ (n) , modulo 2 3 for M(n) and T ∗ (n) , where a = 3 , 4 and ℓ ≥ 1 . For instance, we prove that for n ≥ 0 , P ∗ (5 ℓ (4 n + 3) + 5 ℓ - 1) ≡ 0 (mod 2 3 · 5 ℓ). In addition, we prove witness identities for the following congruences due to Pushpa and Vasuki: M (5 n + 4) ≡ 0 (mod 5) , T ∗ (5 n + 3) ≡ 0 (mod 5). [ABSTRACT FROM AUTHOR] |
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