Pagination for custom query throws 404 errors on last pages [duplicate]

Exactly what @Pieter Goosen said. Not only are you creating havoc for WordPress, you’re adding unnecessary load on the server by introducing more queries on top of the main query:

function wpse_176933_custom_authors_archive( $wp_query ) {
    if ( $wp_query->is_main_query() && $wp_query->is_author() ) {
        $wp_query->set( 'posts_per_page', 4 );
        $wp_query->set( 'post_type', 'publikasjoner' );
        $wp_query->set( 'meta_key', 'rapportnummer' );
        $wp_query->set( 'orderby', 'meta_value_num' );
        $wp_query->set( 'order', 'DESC' );
    }
}

add_action( 'pre_get_posts', 'wpse_176933_custom_authors_archive' );

Add this hook to your functions.php, remove any custom queries from author.php, and replace your custom loop with the main loop functions (the_loop(), the_post() etc.).