The Sanlun school, also known as the Three Treatise school, was a prominent Chinese Madhyamaka school that emerged during the 6th century. It was founded by the Indian monk Kumarajiva and became one of the most influential schools of Chinese Buddhism. The teachings of Sanlun were based on the Madhyamaka philosophy, which emphasized the concept of emptiness and the middle way between extremes. This school had a significant impact on other schools of Chinese Buddhism, and its influence can still be seen in modern Chinese Buddhism.

One of the major ways in which the Sanlun school influenced other schools of Chinese Buddhism was through its emphasis on the study and interpretation of Buddhist scriptures. The Sanlun school placed great importance on the study of the three major treatises of Madhyamaka philosophy - the Madhyamaka-karika, the Shata-shastra, and the Dvadasha-dvara-shastra. This emphasis on scriptural study and interpretation influenced other schools of Chinese Buddhism, such as the Tiantai and Huayan schools, which also placed great importance on the study and interpretation of Buddhist scriptures.

Furthermore, the Sanlun school's emphasis on the concept of emptiness had a profound influence on other schools of Chinese Buddhism. The concept of emptiness, or shunyata, is a central tenet of Madhyamaka philosophy and is also found in other schools of Buddhism, such as Zen and Pure Land. The Sanlun school's teachings on emptiness influenced the development of these schools, particularly in their understanding of the nature of reality and the path to enlightenment.

In addition, the Sanlun school's emphasis on the middle way between extremes had a significant impact on other schools of Chinese Buddhism. This concept of the middle way, or Madhyamaka, was also adopted by the Tiantai and Huayan schools. It became a fundamental principle in these schools, guiding their understanding of the Buddhist path and the nature of reality.

The Sanlun school also played a crucial role in the development of Chinese Buddhist philosophy. Its teachings were highly influential in the formation of the Chinese Buddhist philosophical system, which combined Indian Buddhist thought with Chinese philosophical ideas. The Sanlun school's emphasis on scriptural study and philosophical analysis greatly contributed to the development of this system, which had a lasting impact on Chinese Buddhism.

In conclusion, the Sanlun school had a profound influence on other schools of Chinese Buddhism. Its emphasis on scriptural study, the concept of emptiness, the middle way, and its role in the development of Chinese Buddhist philosophy have shaped the landscape of Chinese Buddhism to this day. The Sanlun school's teachings continue to be studied and practiced by many, making it a significant and enduring influence on Chinese Buddhism.