A Turkish couple living in Riverhead were arrested last Thursday in connection with email messages describing a plot to blow up the Jewish Center of the Hamptons. Agents of the Department of Homeland Security stopped the couple, Asli Dincer, 44, and Melih Dincer, 30, at Kennedy Airport late Thursday as they arrived on a flight from Turkey. They were said to be carrying $31,500 in cash between them when they were arrested. They were questioned by border agents at Terminal One and turned over to East Hampton Village detectives, who placed them under arrest. Police said the couple had made up the threatening emails in an attempt to ensnare a third, unidentified person with whom they had a dispute. The emails indicated there would be an attack on the center during the month of Ramadan, which began on June 28. The couple were arraigned in East Hampton Town Justice Court on Friday and charged with two felonies, making a terror threat and making a false report of such an incident, and two misdemeanors, menacing and conspiracy. According to the complaint, the defendants “sent three emails to the director of the Jewish Center of the Hamptons, making a baseless terroristic threat of the imminent commission of a bombing with intent to commit murder.” Chief Gerard Larsen said the emails warned that the Jewish Center was about to be blown up, and named a foreign national, living in the United States, as complicit. Police are investigating the relationship between the Dincers, who, though reportedly divorced, share the same Riverside address, and the individual named. “One must deal with these things as very serious threats,” Rabbi Sheldon Zimmerman of the Jewish Center said Friday. He said he alerted police as soon as the first email was received, on May 28, and that detectives immediately made contact with the F.B.I., which was involved in the case along with the Joint Terrorism Task Force, the Suffolk Police Department, and New York State police. The center received two more emails from the couple, one on June 3 and the last on June 8. A police car equipped with a license-plate reader was parked in Wainscott on the eastbound shoulder of Montauk Highway for several weeks, before the F.B.I. determined that the threats were baseless. Court papers contained the couple’s statements to agents at the airport. Ms. Dincer was asked if she had sent the emails, and answered that she had. Asked why, she replied that “He tried to mess up my life by saying bad things about me to the old man.” Mr. Dincer also admitted making up the email threats. “I hate this guy,” he told the agents. “He tried to ruin our lives.” He claimed he had acted alone, that “she had nothing to do with it.” Both pleaded not guilty through their attorney, Andrew Wolk of Ronkonkoma, who declined comment. East Hampton Town Justice Steven Tekulsky set bail at $50,000 apiece, but the Department of Homeland Security ordered that the couple remain in custody. “All the authorities have been so helpful,” Rabbi Zimmerman said. “People should know that they are protected.”