The first rental construction in six years in trendy West Hartford Center is expected to begin in a month as two forlorn buildings are torn down to make way for luxury apartments that could test the upper limits of the area’s asking rents. The 48-unit apartment building will replace the buildings at 920 and 924 Farmington Avenue — an area considered the gateway to the heart of the Center. The new rentals could be ready by the fall of 2023. The mixed-use project — expected to cost more than $15 million — has been christened “The Byline” after a writer’s credit at the top of a newspaper story. The name also draws on the town’s legacy of publishing and being the birthplace of Noah Webster. Krohn said the cost of construction is almost double per square foot of other projects in central Connecticut, based on town building requirements.