Acta Mathematica Sinica

, Volume 22, Issue 5, pp 1329–1342 | Cite as

The Exceptional Set in the Two Prime Squares and a Prime Problem

ORIGINAL ARTICLES

Abstract

In this paper we prove that, with at most \( O{\left( {N^{{\frac{5} {{12}} + \in }} } \right)} \) exceptions, all positive odd integers nN with n ≡ 0 or 1(mod 3) can be written as a sum of a prime and two squares of primes.

Keywords

circle method Cauchy’s inequality Siegel zero Dirichlet character 

MR (2000) Subject Classification

11P32 11P55 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Department of MathematicsQufu Normal UniversityQufu 273165P. R. China
  2. 2.Department of Computer ScienceShandong UniversityJi’nan 250100P. R. China
  3. 3.Department of Statistics and MathematicsShandong Finance InstituteJinan 250014P. R. China

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