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In this paper, a Ramanujan-Hardy-Littlewood type identity is derived using the properties of modified Bessel’s function of second kind and of order zero. This identity involved all non-trivial zeros of the Riemann-zeta function. Further, a modular transformation can be observed in this identity in which a real number \(\beta \) is such that \(\beta \rightarrow \frac{1}{\beta }\) .

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Ramanujan-Hardy-Littlewood Type Identity Involving Modified Bessel’s Function

  • 会议论文

  • 发表日期：

    2026年

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  • Saurabh Rana,
  • Vinay Shukla,
  • Himani Bhatt,
  • Mohamed Abdalla

摘要

In this paper, a Ramanujan-Hardy-Littlewood type identity is derived using the properties of modified Bessel’s function of second kind and of order zero. This identity involved all non-trivial zeros of the Riemann-zeta function. Further, a modular transformation can be observed in this identity in which a real number \(\beta \) is such that \(\beta \rightarrow \frac{1}{\beta }\) .