
The quadratic WaringGoldbach problem
 LIU Jianya and ZHAN Tao

J4. 2007, 42(2):
118 .
doi:

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The purpose of this paper is to briefly survey the recent progress towards the quadratic WaringGoldbach problem. Contents of the paper are as follows: the WaringGoldbach problem, the circle method, Hua's theorem with five almost equal prime variables, treatment of the enlarged major arcs, the major arcs in the representation by four squares of primes, meanvalue estimates for Dirichlet polynomials, the minor arcs and exceptional set in the representation by four squares of primes, estimates of exponential sums over primes, sieve methods in the representation by four squares of primes, Lagrange's theorem with almost prime variables, the LinnikGallagher problem, new results for Hua's theorem with five almost equal prime variables, sums of three squares of almost primes, Sarnak's conjecture and ternary quadratic forms.