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The Li coefficients
of a zeta or
provide an equivalent criterion for the (generalized) Riemann hypothesis. In this paper we define these coefficients, and their generalizations, the
-Li coefficients, for a subclass of the extended Selberg class which is known to contain functions violating the Riemann hypothesis such as the Davenport–Heilbronn zeta function. The behavior of the
-Li coefficients varies depending on whether the function in question has any zeros in the half-plane
We investigate analytically and numerically the behavior of these coefficients for such functions in both the
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