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Integers represented as the sum of one prime, two squares of primes and powers of 
Author(s):
Guangshi
Lü;
Haiwei
Sun
Journal:
Proc. Amer. Math. Soc.
MSC (2000):
Primary 11P32, 11P05, 11N36, 11P55
Posted:
September 26, 2008
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Abstract:
In this short paper we prove that every sufficiently large odd integer can be written as a sum of one prime, two squares of primes and  powers of  .
References:
-
- 1.
- P. X. Gallagher, Primes and powers of
 , Invent. Math. 29(1975), 125-142. MR 0379410 (52:315) - 2.
- G. Harman and A. V. Kumchev, On sums of squares of primes, Math. Cambridge Philos. Soc., 140(2006), 1-13. MR 2197572 (2007b:11153)
- 3.
- D. R. Heath-Brown and J.-C. Puchta, Integers represented as a sum of primes and powers of two, Asian J. Math., 6(2002), 535-565. MR 1946346 (2003i:11146)
- 4.
- L. K. Hua, Some results in the additive prime number theory, Quart. J. Math. (Oxford), 9(1938), 68-80.
- 5.
- A.V. Kumchev, On Weyl sums over primes and almost primes, Michigan Math. J., 54(2006), 243-268. MR 2252758 (2007g:11096)
- 6.
- H.Z. Li, The number of powers of
 in a representation of large even integers by sums of such powers and of two primes, Acta Arith., 92(2000), 229-237. MR 1752027 (2000m:11098) - 7.
- H.Z. Li, The number of powers of
 in a representation of large even integers by sums of such powers and of two primes II, Acta Arith., 96(2001), 369-379. MR 1811879 (2002d:11121) - 8.
- H.Z. Li, Representation of odd integers as the sum of one prime, two squares of primes and powers of
 , Acta Arith., 128(2007), 223-233. MR 2313991 - 9.
- Yu. V. Linnik, Primes numbers and powers of two, Trudy Mat. Inst. Steklov., 38(1951), 152-169 (in Russian). MR 0050618 (14:355e)
- 10.
- Yu. V. Linnik, Addition of prime numbers with powers of one and the same number, Mat. Sb.(N. S.), 32(1953), 3-60 (in Russian). MR 0059938 (15:602j)
- 11.
- J.Y. Liu, M.C. Liu and T.Z. Wang, The number of powers of
 in a representation of large even integers (II), Science in China Ser. A, 41(1998), 1255-1271. MR 1681935 (2000c:11164) - 12.
- J.Y. Liu, M.C. Liu and T. Zhan, Squares of primes and powers of
 , Monatsh. Math., 128(1999), 283-313. MR 1726765 (2000k:11110) - 13.
- J.Y. Liu and M.C. Liu, Representation of even integers as sums of squares of primes and powers of
 , J. Number Theory, 83(2000), 202-225. MR 1772613 (2001g:11156) - 14.
- T. Liu, Representation of odd integers as the sum of one prime, two squares of primes and powers of
 , Acta Arith., 115(2004), 97-118. MR 2099833 (2005f:11227) - 15.
- J.Y. Liu and G.S. Lü, Four squares of primes and
 powers of  , Acta Arith., 114(2004), 55-70. MR 2067872 (2005f:11226) - 16.
- J. Pintz and I. Z. Ruzsa, On Linnik's approximation to Goldbach's problem I, Acta Arith., 109(2003), 169-194. MR 1980645 (2004c:11185)
- 17.
- J. Pintz, A note on Romanov's constant, Acta Math. Hungar., 112(2006), 1-14. MR 2251126 (2007d:11117)
- 18.
- X. M. Ren, On exponential sums over primes and applications in the Waring-Goldbach problems, Science in China Ser. A, 48(2005), 785-797. MR 2158973 (2006g:11167)
- 19.
- M.Q. Wang and X.M. Meng, The exceptional set in the two prime squares and a prime problem, Acta Mathematica Sinica (English series), 22(2006), 1329-1342. MR 2251394 (2007d:11118)
- 20.
- T.Z. Wang, On Linnik's almost Goldbach theorem, Science in China Ser. A, 42(1999), 1155-1172. MR 1749863 (2000m:11097)
- 21.
- J. Wu, Chen's double sieve, Goldbach's conjecture and the twin prime theorem, Acta Arith., 114(2004), 215-273. MR 2071082 (2005e:11128)
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Additional Information:
Guangshi
Lü
Affiliation:
Department of Mathematics, Shandong University, Jinan, Shandong, 250100, People's Republic of China
Email:
gslv@sdu.edu.cn
Haiwei
Sun
Affiliation:
Department of Mathematics, Shandong University, Jinan, Shandong, 250100, People's Republic of China
DOI:
10.1090/S0002-9939-08-09603-2
PII:
S 0002-9939(08)09603-2
Keywords:
Squares of primes,
powers of $2$,
circle method.
Received by editor(s):
January 30, 2008,
Received by editor(s) in revised form:
April 4, 2008
Posted:
September 26, 2008
Additional Notes:
This work is supported by the National Natural Science Foundation of China (Grant No. 10701048).
Communicated by:
Ken Ono
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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