If I have pityriasis, will I give it to the people around me?

Officially, no. The cause of pityriasis rosea is unknown, but it may be a virus (because sometimes several people get the rash around the same time). If it is due to a virus, the way it is transmitted from one person to another is also unknown. So, at this time, the rash is not considered contagious. However, knowing human nature, somebody who gets the rash after touching you may blame you for passing it to him!