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Goldbach’s problem. (Das Goldbach’sche Problem.) (German) Zbl 0805.11003
The author presents a historical survey on Goldbach’s problem, i.e. the representation of integers as sums of two or three primes. He sketches the Hardy-Littlewood circle method and the results obtained from it, I. M. Vinogradov’s solution of the ternary Goldbach problem, the implications of sieve methods, and more recent results (for example the estimate of Montgomery-Vaughan for the number of exceptional, non- Goldbach-integers), localized forms on the ternary problem, the deep Heath-Brown hypothetical result (prime twins and Siegel zeros) and others. Finally some open problems are mentioned.

MSC:
11-03 History of number theory
11P32 Goldbach-type theorems; other additive questions involving primes
11P55 Applications of the Hardy-Littlewood method
01-02 Research exposition (monographs, survey articles) pertaining to history and biography
11N35 Sieves
11M20 Real zeros of \(L(s, \chi)\); results on \(L(1, \chi)\)
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