(The Hill) – Sen. Raphael Warnock (D-Ga.) is pulling ahead of his Republican rival Herschel Walker in the Senate race in Georgia, albeit narrowly, according to a WSAV/Emerson College Polling/The Hill survey released Tuesday.

The poll shows Warnock garnering 48% support to Walker’s 46%. That marks a 4-point improvement for the Democratic incumbent since August, when the same poll showed him trailing Walker 44% to 46%.

The poll was conducted from Oct. 4-7, just after a report from The Daily Beast surfaced allegations that Walker had paid for his then-girlfriend to have an abortion in 2009. Walker, who has campaigned as an ardently anti-abortion conservative, has denied the allegations and has threatened to sue The Daily Beast for defamation.

It’s unclear how much — or even if — the allegations against Walker have hurt his standing in the race. The poll didn’t ask respondents whether they had heard the accusations or if they had an opinion on the matter.

What is clear, however, is that Warnock’s support among women is on the rise. Fifty-one percent of women who responded to the poll said that they are backing Warnock compared to 42% who are supporting Walker. That marks a 4-point increase in support for Warnock since August.

Walker, meanwhile, has seen his advantage among men shrink slightly. In August, he held an 8-point edge over Warnock among men. The most recent poll shows that advantage ticking down to 5 percentage points.

Regardless, neither Walker nor Warnock are winning majority support in the race. Under Georgia’s election rules, a candidate must get more than 50% of the vote to win the contest outright. If neither manages to hit that threshold, they’ll advance to a December runoff election.

Despite the allegations against Walker — and Democrats’ efforts to make abortion rights the central issue of the 2022 midterm elections — a plurality of Georgia voters, 40%, said that the economy is the most important factor in how they will cast their ballots in November.

Another 19% listed threats to democracy as their top issue, while only 12% of respondents said abortion access was their most pressing concern.

Still, reproductive rights appear to remain a motivating factor for most Georgians. A majority of voters — 52% — said that the Supreme Court’s decision to overturn Roe v. Wade, the landmark abortion rights case, makes them more likely to vote in November. Another 45% said that it makes no difference in their decision to vote.

Meanwhile, in the race for Georgia governor, Gov. Brian Kemp (R) is holding onto a 5-point lead over his Democratic opponent Stacey Abrams, scoring 51% support to her 46%.

On the national level, President Biden’s approval rating remains underwater, with about 41% of Georgia voters giving him positive marks for his job performance and 52% disapproving of his performance in the White House, according to the poll.

The WSAV/Emerson College/The Hill poll surveyed 1,000 very likely general election voters in Georgia from Oct. 4-7. It has a margin of error of plus or minus 3 percentage points.