• Specify the relationship between self links and base URIs #840 (comment)
• add example of pagination links #834 (comment)
• add example of pagination links #834 (comment)

relative references are simply not allowed.

So, links should be "links": { "self": "http://example.com/link_author/1"} not {"links": { "self": "//link_author/1"}

How about a link such as "links": { "self": "//link_author/1"} discussed in ActiveModel::Serializers