Dixit, AtulAtulDixitRoy, ArindamArindamRoyZaharescu, AlexandruAlexandruZaharescu2025-08-302025-08-302016-03-0110.1016/j.jnt.2015.08.0052-s2.0-84945365254https://d8.irins.org/handle/IITG2025/21374We give character analogues of a generalization of a result due to Ramanujan, Hardy and Littlewood, and provide Riesz-type criteria for Riemann Hypotheses for the Riemann zeta function and Dirichlet L-functions. We also provide analogues of the general theta transformation formula and of recent generalizations of the transformation formulas of W.L. Ferrar and G.H. Hardy for real primitive Dirichlet characters.trueDirichlet L-function | Ferrar | Hardy | Hypergeometric function | Möbius function | Ramanujan | Riemann Hypothesis | Riemann zeta functionArticle385-408March 01, 201613arJournal12WOS:000365928300019