(CNN) -- The judge presiding over Alaska's Senate race challenge is expected to issue a ruling Friday.
Arguments began Wednesday in the legal challenge filed by Joe Miller which asserts that Alaska law prohibits misspelled write-in ballots from being counted and bars the state from applying more lenient standards for write-in ballots than other ballots.
Sen. Lisa Murkowski ran for re-election as a write-in candidate, after losing the Republican primary to Miller.
Five weeks after election day, Miller trails Murkowski by over 10,000 votes.
But a federal court will not allow the election results to be certified until the state court rules.
Joe Miller's lawsuit against the Alaska Division of Elections is expected to be decided in two days.
The Murkowski campaign considers this a positive step toward resolving the case in time for Murkowski to be certified as the winner before the Senate convenes on January 5.
"Mr. Miller today continued his efforts to disenfranchise Alaska voters, and he is continuing these efforts without the possibility of winning the election," Murkowski's campaign manager Kevin Sweeney said, in a statement Wednesday.
"While we are fighting for the fundamental and constitutional principle that every Alaskan's vote should count, we cannot determine exactly what principle Mr. Miller is trying to defend by seeking to take those votes out."
Miller explained his motive, saying, "This is not about my winning or losing. This is about upholding the integrity of the electoral process, and ensuring that the public can be confident in the results."
In a statement, Miller cited concerns that include write-in ballots from precincts that appear to be in the same handwriting and people on the sex offender registry that have been recorded in election registers as having voted.
Calling these "circumstances (that) appear troubling enough to warrant further investigation," Miller said he expects a different result than Murkowski's camp.
"We are confident the court will enforce Alaska law as written, invalidate the illegal standards... and allow us to obtain further information regarding the other apparent improprieties with the election."
Miller's statement also indicated that the Superior Court will stay the effect of any order it enters on Friday to allow the losing side to appeal to the Alaska Supreme Court.