Bulg. J. Phys. vol.50 no.3 (2023), pp. 301-310

A Characterization of Nontrivial Zeros of Riemann Zeta Function

J. Dasan1, S. Sajikumar1, P. Anitha2, V. Hema1
1Department of Mathematics; College of Engineering Trivandrum, Thiruvananthapuram, Kerala, India
2Department of Mathematics; BJM Government College, Chavara, Kollam, Kerala, India
Abstract. In this article, we give a characterization of nontrivial zeros of the Riemann zeta function using two real integrals. Using this characterization we can provide simple proof of the fact that the Riemann zeta function has no nontrivial real zeros. We also establish that this function takes negative values on the real axis within the critical region.

doi: https://doi.org/10.55318/bgjp.2023.50.3.301

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