• Title/Summary/Keyword: Hecke eigenforms

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DIVISIBILITY AND ARITHMETIC PROPERTIES OF CERTAIN ℓ-REGULAR OVERPARTITION PAIRS

  • ANUSREE ANAND;S.N. FATHIMA;M.A. SRIRAJ;P. SIVA KOTA REDDY
    • Journal of applied mathematics & informatics
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    • v.42 no.4
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    • pp.969-983
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    • 2024
  • For an integer ℓ ≥ 1, let ${\bar{B}}_{\ell}(n)$ denotes the number of ℓ-regular over partition pairs of n. For certain conditions of ℓ, 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 2t satisfied by ${\bar{B}}_3(n)$ employing a result of Ono and Taguchi (2005) on nilpotency of Hecke operators.