nt.number theory - Riemann hypothesis generalization names: extended versus generalized?

Hello,

I also agree that the literature is not quite consistent on this topic. I tried to find a published reference on this question and found the following article:

http://www.springerlink.com/content/v563192510820t34/

which is Chapter 5 of a book "The Riemann hypothesis : a resource for the afficionado and virtuoso alike", by Peter Borwein, Stephen Choi, Brendan Rooney and Andrea Weirathmueller, published by the Canadian Mathematical Society.

In the reference above, they use GRH for Dirichlet L-series (section 6.2), and ERH for Dedekind zeta functions (section 6.5). However, to make things more complicated:

1) They mention (in section 6.3) that ERH may be referring to the conjecture for L series of the form
$$sum_{n=1}^infty frac{left(frac{n}{p}right)}{n^s}$$
where $p$ is a prime and $left(frac{n}{p}right)$ is the Legendre symbol. In fact they call this version ERH, and the one for Dedekind zeta functions is called another extended Riemann hypothesis.

2) They mention that the "Grand Riemann hypothesis" (which I had never heard of) refers to L functions of automorphic cuspidal representations.

Alvaro