“This reflects the fear in Mexican society, the collective psychosis about kidnapping,” said Adrienne Bard, an American radio journalist who has lived in Mexico for more than 20 years and who received a call in March from a crying young woman. Shocked, she thought it was her own college-age daughter.

“I totally fell into the trap,” she said.

So have many others. A new hot line set up to deal with the problem of kidnappings in which no one is actually kidnapped received more than 30,000 complaints from last December to the end of February, Joel Ortega, Mexico City’s police chief, announced recently. There have been eight arrests, and 3,415 telephone numbers have been identified as those used by extortionists, he said.

But identifying the phone numbers  they are now listed on a government Web site  has done little to slow the extortion calls. Nearly all the calls are from cellphones, most of them stolen, authorities say.

On top of that, many extortionists are believed to be pulling off the scams from prisons.

Authorities say hundreds of different criminal gangs are engaged in various telephone scams. Besides the false kidnappings, callers falsely tell people they have won cars or money. Sometimes, people are told to turn off their cellphones for an hour so the service can be repaired; then, relatives are called and told that the cellphone’s owner has been kidnapped. Ransom demands have even been made by text message.

Of the relatively few arrests made so far, three suspects were brothers, ages 19, 31 and 34, who were caught collecting money squeezed from a victim. The two younger brothers blamed their older sibling, who has been in and out of prison for years, of putting them up to it.