Abstract : In the
theory of zeta or L- functions it is useful to
have good estimates for $N(\sigma, T, 2T)$, the
number of zeros $\rho = \beta+i\gamma$ for
which $\beta> \sigma$ and $T \lt \gamma \lt
2T$.
In this talk we study zero-density
estimates of various zeta or L- functions. In
particular we introduce that zero-density
estimates of a Hecke L-function are related to a
universality theorem and fractional moments
of the L-function.