The author names mentioned are regarded individually relating to their books. Let's say those five authors (A to E) have each released one book, so five total (Ax to Ex). The person picks up book Bx, and reads the name of author B on the cover, and is then prompted to buy it. For book Cx, it would be a different author, namely C.
Please let me know if this helps, or if you need clarification.
Racked my brain a little following the comment. I'd refer you to the distributive singular as discussed by Quirk et al. in A Comprehensive Grammar of the English Language (10.47 Distributive number):
While the distributive plural is the norm, the distributive singular may also be used to focus on individual instances. We therefore often have a number choice:
- The students raised their hand(s).
- Some children have understanding fathers / an understanding father.
- We all have good appetites / a good appetite.
- Pronouns agree with their antecedent(s).
- Their noses need / nose needs to be wiped.
- The exercise was not good for their back(s).
For some freely accessible context, see this MLA article on distributive plural vs. singular.