Four-term Petersburg Treasurer Carole S. Matthews is being challenged by a political newcomer in next month’s Democratic primary. Businessman Kevin A. Brown, 46, who has 20 years’ experience in commercial finance, promises better customer service, efficiency and transparency at the Treasurer’s Office. Matthews has deep roots in the city, having lived there for 25 years. Brown moved to Petersburg four years ago and is part of an active group of new residents seeking changes in city government.