If you want to get the Author login from the SharePoint object, for example, list item, you should use 'expand=Author' in the query. It's necessary, but not sufficient. There's one more option, which you must use.

A query, which returns the author Email, looks like this:

https://markimarta.sharepoint.com/sites/mysite/_api/web/lists/getByTitle('Answers')/items?$select=ID,Title,UserSlots,Author/EMail&$expand=Author&$filter=+EventId+eq+34

'M' in the word 'EMail' must be capital.

If you think, that the register is not important, it's a big mistake.
if you write in the query "$select=ID,Title,UserSlots,Author/Email&$expand=Author&…", then you have an error like this:

<m:error xmlns:m="http://schemas.microsoft.com/ado/2007/08/dataservices/metadata">
<m:code>-1, Microsoft.SharePoint.SPException</m:code>
<m:message xml:lang="en-US">The query to field 'Author/Email' is not valid.</m:message>
</m:error>

Microsoft is not like Tefal, he doesn't always think of you 🙂