Abstract:     Digital economy provides an important driving force for a new round of industrial transformation and economic growth, and the science and technology service industry is an important emerging industry to optimize the industrial structure and improve economic efficiency. What is the synergistic status and effect of digital economy and the science and technology service industry? To this end, the synergistic development mechanism of the digital economy and the science and technology service industry was analyzed with the Entropy right-Topsis method and the coupling coordination model to study the evolution of the digital economy, the science and technology service industry and their synergy evolution characteristics in 30 provincial-level regions of China, while the two-way fixed effect model and gating effect model were used to empirically test the influence of the synergistic development on the regional economic efficiency in China. The research findings were as follows: from 2012 to 2019, the development index of the digital economy and the science and technology service industry in 30 provincial-level regions showed an obvious rising trend, presented a distinct heterogeneity in space, and the eastern region is higher than that of the central and western regions and the northeast regions; the synergistic level between the digital economy and the science and technology service industry continues to improve. In 2012, the number of 22 provincial-level regions were located in the lose balance and drop behind range, and the number decreased to 10 in 2019, it is characterized by "high and high agglomeration" and "low and low agglomeration" in the geographical distribution of the digital economy and the science and technology service industry. The synergistic development of the digital economy and the science and technology service industry positively affects the regional industrial labor productivity, industrial pure technology efficiency and GDP growth rate, and brings a negative impact on the regional investment efficiency. This paper explored the spatial and temporal evolution characteristics, synergistic mechanism and influence effect of the synergistic development of the digital economy and the science and technology service industry from the perspective of industrial correlation, and it will enrich the relevant innovation theory research, and grasp the situation of regional digital economy, science and technology service industry, the synergistic development of the two, thus optimizing the development planning and policies of the digital economy in various regions and improving the level of scientific and technological services has a positive promoting effect.

Key words: digital economy, science and technology service industry, synergistic development of industries, regional synergy effect