This is the 18244th most frequent Russian word.
читателям
"Readers" (dative plural form).
The word 'читателям' is used here as a dative plural noun that denotes the audience for whom the book is intended.
Эта книга предназначена читателям, интересующимся историей.
This book is intended for readers interested in history.
Here, 'читателям' is used in the dative plural form to denote the recipients of the autographs.
Авторы книги подарили автографы своим читателям.
The authors of the book gave autographs to their readers.
In this example, 'читателям' is again in the dative plural, representing the recipients of the thank-you letters.