NEW YORK (AP) ― Not many people owned a copy of “The Cuckoo’s Calling’’ before word leaked out over the weekend that author Robert Galbraith was, in fact, J.K. Rowling.

But among those who did, a handful managed to get a signed edition. And that could mean a lot of money.

Rowling spokeswoman Nicky Stonehill told The Associated Press on Tuesday that Rowling, the “Harry Potter’’ author, signed “a few copies’’ of her detective novel as “Robert Galbraith.’’ Wishing to keep her identity secret, Rowling made no promotional appearances for the book, published quietly in April, and Stonehill declined to say how any reader obtained a signed copy.

Bids for a signed first edition have topped $3,000 on eBay by Tuesday evening.

“Yes, those books will have value,’’ said Angel Webster of Bauman Rare Books in Manhattan. “The first edition is already a scarce commodity and she only signed a handful of them under vague circumstances.’’

Webster added that it was too soon to know how much money a signed first edition might be worth. Signed first editions of the first “Harry Potter’’ book, published in 1997 in England as “Harry Potter and the Philosopher’s Stone,’’ are worth thousands of dollars.

Webster said the value of a signed “Cuckoo’s Calling’’ will depend on how well the novel ends up selling and whether it becomes the first book of a series.

“The Cuckoo’s Calling’’ received favorable reviews when it first came out but attracted little attention from the general public. It is now No. 1 on Amazon.com, and publisher Little, Brown and Company has commissioned a new printing of 300,000 copies. Sellers have been out of stock, and frustrated by the delay in receiving new books, which may take as long as two to three weeks to arrive.

“We’re in the same boat as other bookstores in this country ― out and waiting for reprints,’’ said Gayle Shanks, co-founder of Changing Hands Bookstore in Tempe, Arizona.

The novel features London detective Cormoran Strike. Little, Brown has announced that a second Strike novel is planned for next summer.