Looking at the Selberg class definition on Wikipedia, under "Comment on definition", there is this paragraph:

"The condition that the real part of $\mu_i$ be non-negative is because there are known L-functions that do not satisfy the Riemann hypothesis when $\mu_i$ is negative. Specifically, there are Maass forms associated with exceptional eigenvalues, for which the Ramanujan–Peterssen conjecture holds, and have a functional equation, but do not satisfy the Riemann hypothesis."

$\mu_i$ is a constant in the Gamma factor which is part of the functional equation.

I am looking for an article reference or book showing this particular Maass for which RH is wrong.

Below is the link to Wikipedia article where there is no reference supporting this result.

https://en.wikipedia.org/wiki/Selberg_class.

Looking at the Selberg class definition on Wikipedia, under "Comment on definition", there is this paragraph:

"The condition that the real part of $\mu_i$ be non-negative is because there are known L-functions that do not satisfy the Riemann hypothesis when $\mu_i$ is negative. Specifically, there are Maass forms associated with exceptional eigenvalues, for which the Ramanujan–Petersson conjecture holds, and have a functional equation, but do not satisfy the Riemann hypothesis."

$\mu_i$ is a constant in the Gamma factor which is part of the functional equation.

I am looking for an article reference or book showing this particular Maass for which RH is wrong.

Below is the link to Wikipedia article where there is no reference supporting this result.

https://en.wikipedia.org/wiki/Selberg_class.

Looking at Selberg Class definition on Wikipedia, under "Comment on definition", there is this paragraph:

"The condition that the real part of $\mu_i$ be non-negative is because there are known L-functions that do not satisfy the Riemann hypothesis when $\mu_i$ is negative. Specifically, there are Maass forms associated with exceptional eigenvalues, for which the Ramanujan–Peterssen conjecture holds, and have a functional equation, but do not satisfy the Riemann hypothesis."

$\mu_i$ is a constant in the Gamma factor which is part of the functional equation.

I am looking for an article reference or book showing this particular Maass for which RH is wrong.

Below is the link to Wikipedia article where there is no reference supporting this result.

https://en.wikipedia.org/wiki/Selberg_class#:~:text=In%20mathematics%2C%20the%20Selberg%20class,L%2Dfunctions%20or%20zeta%20functions.

Looking at the Selberg class definition on Wikipedia, under "Comment on definition", there is this paragraph:

"The condition that the real part of $\mu_i$ be non-negative is because there are known L-functions that do not satisfy the Riemann hypothesis when $\mu_i$ is negative. Specifically, there are Maass forms associated with exceptional eigenvalues, for which the Ramanujan–Peterssen conjecture holds, and have a functional equation, but do not satisfy the Riemann hypothesis."

$\mu_i$ is a constant in the Gamma factor which is part of the functional equation.

I am looking for an article reference or book showing this particular Maass for which RH is wrong.

Below is the link to Wikipedia article where there is no reference supporting this result.

https://en.wikipedia.org/wiki/Selberg_class.