In addition to asking for autographs in person, I think you can also send what you want to sign to their record company, such as photos, and attach an envelope with your own address, which will minimize the trouble of the other party and make you more willing to sign.

However, it should be noted that some stars' brokerage systems do not allow them to sign their names at will. For example, F4 is Japanese, and does not sign for fans, because in the concept of brokerage company, signing is a kind of "value-added" business behavior, and an ordinary photo can be resold at a higher price after signing, so it will be rejected unless it is indicated that it will sign for fans at a specific event. But I don't think Jay Chou is one of them. If he receives the letter and is in a good mood, he may sign it (just don't expect too much). If every fan does this, he will probably sign to break the contract.