JON O. NEWMAN, Circuit Judge.

This appeal concerns the circumstances under which an arbitrator or a court may take steps to have an arbitration award corrected. The correction concerns the identity of the party against whom an arbitrator ordered relief. William H. Hyle, Jr. appeals from the March 31, 1999, judgment of the District Court (Peter C. Dorsey, District Judge), denying Hyle’s motions to confirm an original arbitration award that ordered damages and injunc-tive relief only against his business partner Michael Gruelich and to vacate a “corrected” arbitration award that ordered such relief only against Hyle. The judgment also remanded for clarification in accordance with the District Court’s ruling. We conclude that the District Court should have remanded to the arbitrator, without restriction, so that the arbitrator could determine whether a correction was warranted. Accordingly, we affirm in part, modify in part, and remand.

Background

Hyle, the Plaintiff-Appellant, Gruelich, and two other partners entered into a franchise agreement with the Defendant-Appellee, Doctor’s Associates, Inc. (“DAI”) to operate a Subway fast-food establishment. DAI filed an arbitration demand with the American Arbitration Association (“AAA”) against Hyle and his partners to terminate the franchise agreement and to obtain damages and injunctive relief. DAI claimed that the four respondents named in the arbitration demand had breached their franchise agreement by operating a sandwich shop known as “Your Way Café” in Baltimore and using Subway trademark items at that shop.

At the arbitration hearing, Hyle was the only respondent who appeared. At the start of the hearing, DAI stated that it was seeking a termination of the franchise agreement with respect to all four respondents but was seeking damages and an injunction only against Hyle, because only Hyle was involved in operating the sandwich shop in Baltimore. On March 30, 1998, the arbitrator entered an award in favor of DAI. The arbitrator terminated the franchise agreement, awarded $19,-210.56 in lost royalties, and prohibited the use of Subway materials in the Baltimore sandwich shop, subject to a $100 per day fine for violation, with a maximum fine of $219,000. In apparent disregard of DAI’s announced position to seek damages and injunctive relief only against Hyle, the award of damages and injunctive relief was entered only against Gruelich. The AAA sent the award to DAI and Gruelich on April 1. Gruelich sent a copy of the award to Hyle shortly thereafter.

In a letter dated April 22, 1998, DAI’s counsel wrote to the AAA seeking “clarification” on whether the arbitrator intended to name Gruelich individually, Hyle individually, or all four respondents. The AAA’s response stated, “An arbitration award is considered final when rendered and the arbitrator’s authority ceases thereafter. The parties, by written consent, may reinstate the authority of the arbitrator.” The AAA sent this letter to DAI’s counsel and Gruelich, but not to Hyle. The AAA subsequently forwarded the letter to the arbitrator.

In a letter dated May 19, 1998, the arbitrator responded to the AAA, stating that while the part of the award terminating the franchise agreement covered all the respondents, the award of damages and injunctive relief was intended to cover only Hyle. As the arbitrator explained:

This was based upon the oral statement made by Doctors Associates at the be *370 ginning of the hearing that while they sought a termination order as to all defendants, they were seeking monetary damages and injunctive relief only against the appearing witness, William Hyle, Jr. This limitation was accepted by me, without objection from Mr. Hyle. When I reviewed my original notes, I verified it was Mr. Hyle testifying, not Mr. Gruelich. Therefore, I have corrected the award.

The arbitrator issued a “Corrected Arbitration Award” replacing Gruelich’s name with Hyle’s name in the paragraphs pertaining to damages and injunctive relief. Hyle claimed that he did not receive the letters between the AAA, DAI, and the arbitrator until he requested them from the AAA on August 17, 1998. Hyle also claimed that he did not discover that the award had been resubmitted to the arbitrator until July 1998, when he received a copy of the “Corrected Arbitration Award.”

On August 18, 1998, Hyle filed the instant action to confirm the original arbitration award pursuant to 9 U.S.C. § 9 as to himself and DAI only (i.e., to confirm that he had not been ordered to pay damages or be subject to an injunction), and to vacate the “Corrected Arbitration Award” pursuant to 9 U.S.C. § 10. DAI moved to remand the matter to the AAA for clarification. The District Court denied Hyle’s motions and, in light of what the Court characterized as “clearly a simple mistake” in subjecting Gruelich rather than Hyle to a damages award and injunctive relief, remanded the matter to the AAA “for clarification of the award in accordance with this ruling.”

Discussion

The issue on this appeal arises in an area of arbitration law where four related rules of law converge. First, absent an agreement by the parties to the contrary, “once arbitrators have finally decided the submitted issues, they are, in common-law parlance, ‘functus officio,’ meaning that their authority over those questions is ended.” Trade & Transport, Inc. v. Natural Petroleum Charterers Inc., 931 F.2d 191, 195 (2d Cir.1991). Second, even after rendering an award, an arbitrator retains limited authority to “correct a mistake which is apparent on the face of [the] award.” Colonial Penn Insurance Co. v. Omaha Indemnity Co., 943 F.2d 327, 332 (3d Cir.1991) (internal quotation omitted). “The exception for mistakes apparent on the face of the award is applied to clerical mistakes or obvious errors in arithmetic computation.” Id. at 332 (citation omitted); see Local P-9, United Food & Commercial Workers v. George A. Hormel & Co., 776 F.2d 1393, 1394 (8th Cir.1985). Third, a district court also has limited authority to correct certain mistakes — “an evident material miscalculation of figures or an evident material mistake in the description of any person, thing, or property referred to in the award.” 9 U.S.C. § 11(a) (1994). Fourth, a district court can remand an award to the arbitrator for clarification where an award is ambiguous. See Colonial Penn, 943 F.2d at 333-34; Americas Insurance Co. v. Seagull Compania Naviera, S.A., 774 F.2d 64, 67 (2d Cir.1985).

In the pending case, DAI contends that the arbitrator had “inherent” authority to correct what it regards as the “obvious error” in subjecting Gruelich, instead of Hyle, to the damages award and the injunction. Brief for Appellee at 11. DAI relies on Laurin Tankers America, Inc. v. Stolt Tankers, Inc., 36 F.Supp.2d 645 (S.D.N.Y.1999), which permitted an arbitrator to make a correction arguably beyond the usually limited circumstances for such corrections. The Appellee therefore contends that the District Court’s rulings refusing to confirm the first award and remanding the matter to the AAA should be affirmed. The Appellant contends that the arbitrator lacked authority to issue the “corrected” award and that the District Court lacked authority to remand the matter because DAI did not move to modify *371 that award within the three month period specified in 9 U.S.C. § 12. The Appellant therefore contends that both rulings of the District Court should be reversed and that the original award should be confirmed.

The District Court reached the result favored by the Appellee, but did not precisely adopt the Appellee’s approach. The Court concluded that the designation of Gruelich, rather than Hyle, as the respondent against whom an injunction and damages were awarded, was “a simple mistake.” For that reason, the Court denied Hyle’s motion to confirm the original award and to vacate the “corrected” award. Then, rejecting the Appellee’s motion to remand “for clarification,” the Court remanded “for clarification of the award in accordance with this ruling.”

It is arguable that the designation of Gruelich, rather than Hyle, as the respondent against whom the award ordered damages and an injunction was, as the District Court ruled, a “mistake,” but if so characterized, the issue would then arise whether this is the sort of “mistake” that may be corrected by an arbitrator or ordered to be corrected by a court. The argument would emphasize that DAI’s narrowing of its demand for relief at the start of the hearing amounted to an amendment of the “pleadings,” and that the naming of Hyle, rather than Gruelich, in the award was a mistake on the face of the award when read in conjunction with the amended pleadings. To the extent that such an argument would be advanced to justify the Court’s direction to modify the award, the argument would encounter Hyle’s contention that DAI has not moved for modification within section 12’s three-month period, to which DAI responds that the time limit should not be enforced in the circumstances of this case.

We analyze the problem somewhat differently than do the parties and the District Court. We think the wording of the award, read in conjunction with the undisputed limitation announced by DAI as to the respondent against whom it was seeking damages and an injunction, creates an ambiguity as to whether the arbitrator intended to award damages and an injunction against Gruelich, Hyle, or possibly even all four respondents. See Colonial Penn, 943 F.2d at 334 (“[A]n ambiguity in the award for which the court may remand to the arbitrators may be shown not only from the face of the award but from an extraneous but objectively ascertainable fact.”). That ambiguity sufficed to justify the District Court’s denial of Hyle’s motion to confirm the original award and also provided an occasion for the Court to remand to have the ambiguity resolved. 1 See Ottley v. Schwartzberg, 819 F.2d 373, 376 (2d Cir.1987). Though the arbitrator has now indicated in his “corrected” award what he intended to order, he acted at a time when he might have lacked authority, and the District Court might have lacked authority to direct compliance with the arbitrator’s expressed intention. Accordingly, a remand “for clarification in accordance with [the District Court’s] ruling,” though entirely understandable, risks exceeding the authority of the District Court. The more prudent course is to have the District Court remand to the AAA, without restriction, to permit the arbitrator to resolve the ambiguity as to the identity of the person or persons intended to be subject to the award’s remedy. Cf. Boyko v. Anderson, 185 F.3d 672, 675-76 (7th Cir.1999) (re *372 mand to District Court to make modification of judgment under Fed.R.Civ.P. 60(b) that District Court had made, without jurisdiction, after notice of appeal had been filed); Smith v. Lujan, 588 F.2d 1304, 1308 (9th Cir.1979) (same as to modification of judgment under Fed.R.Civ.P. 60(a)). 2

Accordingly, the ruling of the District Court denying confirmation of the original award is affirmed, and the ruling remanding to the AAA for clarification in accordance with the District Court’s ruling is modified to provide that the remand is made, without restriction, to afford the arbitrator an opportunity to resolve the ambiguity concerning the remedy. In light of this disposition, the appeal from the ruling declining to vacate the corrected award is dismissed as moot. No costs.

Notes

. The District Court's authority to remand to eliminate the ambiguity in the award is not barred by the three month limit on the time for a motion to "vacate, modify, or correct” an award. See 9 U.S.C. § 12. A remand to eliminate an ambiguity does not "vacate, modify, or correct” an award; it returns the award to the arbitrator for whatever change the arbitrator might make to resolve the ambiguity. The three month limit is not applicable to such a remand. See Lanier v. Old Republic Insurance Co., 936 F.Supp. 839, 854 (M.D.Ala.1996). Moreover, there is a strong argument that the arbitrator’s corrected award, even if beyond his authority (absent a remand), was a circumstance that would have tolled the three month period, if otherwise applicable.

. Like most circuits, see Boyko, 185 F.3d at 675 (collecting cases), we have recently recognized the power of a district court to deny a Rule 60(b) motion after the filing of a notice of appeal from the judgment sought to be modified, see, e.g., Selletti v. Carey, 173 F.3d 104, 109 (2d Cir.1999); Toliver v. County of Sullivan, 957 F.2d 47, 49 (2d Cir.1992), notwithstanding an earlier contrary authority, see Weiss v. Hunna, 312 F.2d 711, 713 (2d Cir.1963), which had previously been cited with apparent approval, see New York State National Organization for Women, 886 F.2d 1339, 1349-50 (2d Cir.1989); Contemporary Mission, Inc. v. United States Postal Service, 648 F.2d 97, 107 (2d Cir.1981).