ORDER
Christopher Poremba, a Michigan state prisoner, appeals pro se a district court judgment denying his petition for a writ of habeas corpus, filed pursuant to 28 U.S.C. § 2254. This case has been referred to a panel of the court pursuant to Rule *18734(j)(l), Rules of the Sixth Circuit. Upon examination, this panel unanimously agrees that oral argument is not needed. Fed. R.App. P. 34(a).
Poremba was convicted following a 1996 jury trial of second degree murder and felony firearm; he was sentenced to fifteen to thirty and two years of imprisonment. The crime occurred when Poremba was physically confronted by his roommate over his behavior toward a third man’s female companion. The third man was also present at the confrontation, and attempted to restrain Poremba’s roommate. Poremba fatally shot his roommate in the chest while he was holding Poremba up against a wall. His conviction was affirmed on direct appeal in the state courts. Poremba then filed for federal habeas corpus relief, raising the same claims he had presented to the state courts. The district court denied the petition after consideration of the merits. The district court also denied Poremba’s motion to alter or amend judgment, in which he sought to raise a new claim regarding the jury instruction on self defense that had not been exhausted in the state courts. The district court then certified two of the claimed errors raised in the original petition for appeal: the introduction of prejudicial character evidence, and the jury instruction on reasonable doubt. This court declined to certify any of the remaining issues. The two issues certified have now been briefed. In his brief, Poremba also attempts to raise the claim he attempted to add in his motion to alter or amend below. Respondent argues that the claimed evidentiary error was not exhausted as a federal claim in the state courts, and addresses the jury instruction error on the merits.
Initially, we conclude that the district court properly addressed the merits of the evidentiary ruling challenged here, because Poremba’s citation to the Constitution in his briefs at the state court level provided the state courts with a full and fair opportunity to rule on the constitutional claim presented. See Rust v. Zent, 17 F.3d 155, 160 (6th Cir.1994).
The state court of appeals found the admission of the prejudicial character evidence regarding Poremba’s drinking habits, womanizing, and obsession with violent movies to be harmless error. In order to be entitled to federal habeas corpus relief, Poremba must demonstrate that the state court’s adjudication of his claim was contrary to or an unreasonable application of clearly established federal law. Franklin v. Francis, 144 F.3d 429, 433 (6th Cir.1998). Generally, errors in evidentiary rulings are not cognizable in federal habeas corpus proceedings unless they denied the defendant a fundamentally fair trial. Kelly v. Withrow, 25 F.3d 363, 370 (6th Cir.1994). In this case, the state court found that the prejudicial character evidence was erroneously admitted, but found the error harmless. The district court concluded that the error could not have substantially influenced the jury’s decision, O’Neal v. McAninch, 513 U.S. 432, 438, 115 S.Ct. 992, 130 L.Ed.2d 947 (1995), because the evidence was not material to the issue of whether Poremba was acting in self defense, as he claimed. We conclude that the state court’s adjudication of this claim was not contrary to or an unreasonable application of clearly established federal law.
Poremba’s second claim challenges the jury instruction defining reasonable doubt. A claimed error in a jury instruction warrants habeas corpus relief only where the conviction violates due process. Estelle v. McGuire, 502 U.S. 62, 72, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991). The Supreme Court has held that the Constitution does not require that any particular *188words be used in defining reasonable doubt, so long as the concept is correctly conveyed. Victor v. Nebraska, 511 U.S. 1, 5, 114 S.Ct. 1239, 127 L.Ed.2d 583 (1994). This court has upheld the same instruction challenged here under this standard. Binder v. Stegall, 198 F.3d 177, 179 (6th Cir.1999). Therefore, this claim is without merit.
Finally, we note that Poremba has attempted to argue his claim regarding the instruction on self defense, which the district court refused to allow him to raise in a post-judgment motion because it had not been exhausted in the state courts. Neither the district court nor this court certified this issue for appeal, and we therefore need not consider it.
For the above reasons, the district court’s judgment is affirmed. Rule 34(j)(2)(C), Rules of the Sixth Circuit.