S2CID 253977494. Bourgain, J. More on the sum-product phenomenon in prime fields and its applications. Int. J. Number Theory 1 (2005), no. 1, 1–32. Bourgain, J.;
circa 1920 The episcopal residence in 1913 Catholic Church in Sichuan St. Joseph's Cathedral, Chongqing Immaculate Conception Cathedral, Chengdu Chinese:
generalizations for the Weyl and Vinogradov results were proven by Jean Bourgain in 1988. Specifically, Khinchin showed that the identity lim n → ∞ 1 n
results in additive combinatorics are an improvement of a result of Jean Bourgain of the size of arithmetic progressions in sumsets, as well as a proof of