A modular relation involving non-trivial zeros of the Dedekind zeta function, and the generalized Riemann hypothesis

Dixit, AtulAtulDixitGupta, ShivajeeShivajeeGuptaVatwani, AkshaaAkshaaVatwani2025-08-312025-08-312022-11-1510.1016/j.jmaa.2022.1264352-s2.0-85132871588https://repository.iitgn.ac.in/handle/IITG2025/25865We give a number field analogue of a result of Ramanujan, Hardy and Littlewood, thereby obtaining a modular relation involving the non-trivial zeros of the Dedekind zeta function. We also provide a Riesz-type criterion for the Generalized Riemann Hypothesis for ζ<inf>K</inf>(s). New elegant transformations are obtained when K is a quadratic extension, one of which involves the modified Bessel function of the second kind.en-USfalseBessel function | Dedekind zeta function | Generalized Riemann hypothesis | Modular relation | Riesz-type criterionA modular relation involving non-trivial zeros of the Dedekind zeta function, and the generalized Riemann hypothesisArticle1096081315 November 202251264357WOS:000833524000008