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On some new arithmetic properties of certain restricted color partition functions.

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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]
Copyright of Arabian Journal of Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Label: Title
  Group: Ti
  Data: On some new arithmetic properties of certain restricted color partition functions.
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  Data: <searchLink fieldCode="AR" term="%22Dasappa%2C+Ranganatha%22">Dasappa, Ranganatha</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ddranganatha@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Channabasavayya%22">Channabasavayya</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Keerthana%2C+Gedela+Kavya%22">Keerthana, Gedela Kavya</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Arabian+Journal+of+Mathematics%22">Arabian Journal of Mathematics</searchLink>. Aug2024, Vol. 13 Issue 2, p275-289. 15p.
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  Data: *<searchLink fieldCode="DE" term="%22PARTITION+functions%22">PARTITION functions</searchLink><br />*<searchLink fieldCode="DE" term="%22ARITHMETIC%22">ARITHMETIC</searchLink><br />*<searchLink fieldCode="DE" term="%22MATHEMATICS%22">MATHEMATICS</searchLink><br />*<searchLink fieldCode="DE" term="%22GEOMETRIC+congruences%22">GEOMETRIC congruences</searchLink><br />*<searchLink fieldCode="DE" term="%22COLOR%22">COLOR</searchLink><br />*<searchLink fieldCode="DE" term="%22WITNESSES%22">WITNESSES</searchLink><br />*<searchLink fieldCode="DE" term="%22EISENSTEIN+series%22">EISENSTEIN series</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Arabian Journal of Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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    Identifiers:
      – Type: doi
        Value: 10.1007/s40065-024-00458-z
    Languages:
      – Code: eng
        Text: English
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        PageCount: 15
        StartPage: 275
    Subjects:
      – SubjectFull: PARTITION functions
        Type: general
      – SubjectFull: ARITHMETIC
        Type: general
      – SubjectFull: MATHEMATICS
        Type: general
      – SubjectFull: GEOMETRIC congruences
        Type: general
      – SubjectFull: COLOR
        Type: general
      – SubjectFull: WITNESSES
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      – SubjectFull: EISENSTEIN series
        Type: general
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      – TitleFull: On some new arithmetic properties of certain restricted color partition functions.
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            NameFull: Channabasavayya
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            NameFull: Keerthana, Gedela Kavya
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            – D: 01
              M: 08
              Text: Aug2024
              Type: published
              Y: 2024
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