Inked for Life

A fascinating explanation is offered by the Prisha in what we say on Rosh Hashana.

He informs us that there is a sefer in Heaven called “שנה טובה” and there it is written those who merit life. Therefore, the Tur writes we are accustomed in Ashkenaz that each person says to his friend that he should be written for a good year (תכתב בשנה טובה). The Tur doesn’t say לשנה טובה, because each person blesses his friend that he should be written in the sefer “שנה טובה.”

Orach Chaim 582:15. Orach Chaim 582:9. Otzar Hayedios, Volume 2.