I have a question about the terminology for special values of L-functions. Is the following a correct description of standard usage:

Suppose L(s) is an L-function which satisfies a functional equation relating $s$ to $w+1-s$, where $w$ is the (motivic) weight.

1. If $m$ is an integer then $L(m)$ is a special value of the L-function.

2. If $m$ is an integer and neither $m$ nor $w+1-m$ is a pole of a $\Gamma$-factor of the L-function, then $m$ is a critical point and $L(m)$ is a critical value of the L-function.

3. $L(\frac{w+1}{2})$ is the central value of the L-function.

4. If $\frac{w+1}{2}$ is not an integer, then the central value is not a special value.

I am pretty sure 2) is correct, unless Deligne's notion of critical point is not the only one. I am also pretty sure 3) is correct, since the central point of the functional equation is pretty unambiguous. It is 1) and 4) that I am hoping the experts can clarify.

I have a question about the terminology for special values of L-functions. Is the following a correct description of standard usage:

Suppose L(s) is an L-function which satisfies a functional equation relating $s$ to $w+1-s$, where $w$ is the (motivic) weight. ADDED LATER: I am assuming the L-function is motivic, otherwise (please correct me if I am wrong) there is nothing special about the value at any integer.

1. If $m$ is an integer then $L(m)$ is a special value of the L-function.

2. If $m$ is an integer and neither $m$ nor $w+1-m$ is a pole of a $\Gamma$-factor of the L-function, then $m$ is a critical point and $L(m)$ is a critical value of the L-function.

3. $L(\frac{w+1}{2})$ is the central value of the L-function.

4. If $\frac{w+1}{2}$ is not an integer, then the central value is not a special value.

I am pretty sure 2) is correct, unless Deligne's notion of critical point is not the only one. I am also pretty sure 3) is correct, since the central point of the functional equation is pretty unambiguous. It is 1) and 4) that I am hoping the experts can clarify.