## 2 Literature Review and Theoretical Analysis
In addition, in manufacturing-intensive areas, producer services are also very likely to form agglomeration. Manufacturing and producer services can form synergistic development through input-output correlation effects. The participation of producer services in all aspects of manufacturing will effectively exert economies of scale, and reduce production and transaction costs. The investment of high-polluting and energy-consuming resources promotes production and manufacturing to move towards a green, low-carbon, and environmentally friendly direction, thereby reducing environmental pollution, improving resource utilization efficiency, and reducing carbon emissions. Secondly, whether it is diversified agglomeration or specialized agglomeration, the agglomeration of productive service industries can play a sharing effect, a learning effect, and a matching effect, enhance the technical cooperation and knowledge diffusion of enterprises in the agglomeration area, and produce knowledge spillover effects. Producer service industry is a typical knowledge- and technology-intensive industry. In the process of agglomeration, it is very easy to infiltrate advanced production technology, ideas, experience, and methods into traditional manufacturing industry through formal and informal channels, and subtly improve enterprise technology levels and productivity [29]. In addition, the agglomeration of producer services will also create a good environment for collective learning and innovation through close cooperation with the upstream and downstream of the manufacturing industry and promote the overall improvement of factor productivity under the effect of technology spillover effects, so as to achieve the goal of reducing carbon emissions. In China, the overall technological innovation capability of the manufacturing industry is low, and the efficiency of resource utilization is not high. As an independent industry characterized by technology-intensive and knowledge-intensive characteristics, the spatial agglomeration of the producer service industry will attract various types of high-tech enterprises. In addition, the specialized agglomeration of the producer service industry, especially financial institutions, and scientific research institutes, can provide necessary financial and technical support for the improvement of manufacturing innovation capabilities, and its diversified agglomeration can provide a good external environment for technological innovation. It is worth noting that the agglomeration of producer services not only has an impact on environmental pollution in the region but may also have obvious spatial spillover effects. With the rapid development of the economy, the agglomeration of producer services can easily break through the limitations of geographical space and traditional industries, which may increase the speed of the optimization of the industrial structure in adjacent regions. It also can promote the separation of producer services in adjacent regions from the manufacturing industry. It is embedded in the value chain of the manufacturing industry, which optimizes the internal organizational structure of the manufacturing industry and gradually develops towards an environmentally friendly direction [30]. In this process, the reduction of the proportion of production and manufacturing will be accompanied by the reduction of energy consumption, which will promote the effective improvement of environmental pollution in adjacent areas. It can be seen that the agglomeration of producer services can have spillover effects on environmental improvement through the optimization of industrial structure. The mechanism by which the productive service industry affects carbon emissions is shown in Figure 1.