A Bound For The Representability Of Large Numbers By Ternary Quadratic Forms And Nonhomogeneous Waring Equations

摘要

The solvability of the equation n = x~2 + y~2 +6pz~2 (p is a fixed large prime) is proved under some natural congruential conditions and the assumption nm~(12) > p~(21). As an implication, the solvability of the equation n = x~2 + y~2 + u~3 + v~3 + z~4 + w~(16) + t~(4k+1) for all sufficiently large n is established. Bibliography: 13 titles.