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On the representation of large odd integer as a sum of three almost equal primes

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Abstract

The well-known Goldback-Vinogradov theorem states that every large odd integer is a sum of three primes. In the present paper it is further proved that every large odd integerN can be represented as

$$N = p_1 + p_2 + p_3 , with p_i = N/3 + O(N^{{5 \mathord{\left/ {\vphantom {5 6}} \right. \kern-\nulldelimiterspace} 6}} (\log N)^c )$$

wherc>0 is an absolute constant, andp i (1≦i≦3) are primes. The result is obtained by means of Hardy-Littlewood circle method, Heath-Brown's identity and power moments of DirichletL-functions over short intervals.

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Authors and Affiliations

  1. Institute of Mathematics, Shandong University, Jinan

    Zhan Tao

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  1. Zhan Tao
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The Project Supported by National Natural Science Foundation of China

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Tao, Z. On the representation of large odd integer as a sum of three almost equal primes. Acta Mathematica Sinica 7, 259–272 (1991). https://doi.org/10.1007/BF02583003

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  • DOI: https://doi.org/10.1007/BF02583003

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