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The reconfigurable intelligent surface (RIS), which consists of many low-cost reflecting elements, can enhance the reception of the desired signal and suppress the interference. Considering the above advantages, this paper investigates the RIS-assisted wireless communication in the presence of an interferer, where a receiver receives the desired signal and interference from a transmitter and an interferer, respectively, and the RIS is deployed to assist this system. First, an interference-limited channel capacity maximization problem is formulated, and a numerical algorithm based on the fraction programming and optimality conditions is proposed to obtain the optimal solution. Then, this paper shows the upper boundary of the maximal capacity with interference and discusses what kind of channel conditions can achieve the upper boundary and the corresponding optimal phase shifts. Next, this paper analyzes the asymptotic behaviors of the maximal capacity in the scenarios that some or all of the number of reflecting elements, antennas at the transmitter, and interferer go to infinity. Finally, this paper generalizes the above results to the multiple interferers scenario. [ABSTRACT FROM AUTHOR]