ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

3. Number Theory and Arithmetic Algebraic Geometry

1991 MS Classification: 11, 60, 62 Wu, Xinsheng, The 16th Research Institute Of The Ministry of Electronics Industry, P. R. China The Generalization of Prime Theorem Suppose 2n(n > 2). Is there a function f(2n) to be only dependent upon 2n? It can express a number of group of prime solutions on representation of even integer as a sum of two primes. In one-dimensional space, prime theorem is led into odd sequence integer:

P (G) ∼ \frac{2}{log n}in G = \{1, 3, 5, …, \} are from π(n) . P_{2n}(1, 1) is solved by

P (G). The prime theorem is generalized into two-dimensional space: a

prime joint density is P (P_{x}, P_{y}) ∼ \frac{1}{log x log y} · π(x.y) = ∫ ∫_{S=xy} \frac{dt_{1}dt_{2}}{log t_{1} log t_{2}} .

A number of prime spots (P_{x}, P_{y}) in a circle can be estimated by π(x, y), and P_{2n}(1, 1)_{2} has a result. Results of P_{2n}(1, 1) and P_{2n}(1, 1)_{2} are two mathematical models. Their laws are unanimous. This is a direct answer to Goldbach’s conjecture.