Integers represented as the sum of one prime, two squares of primes and powers of $2$
HTML articles powered by AMS MathViewer
- by Guangshi Lü and Haiwei Sun
- Proc. Amer. Math. Soc. 137 (2009), 1185-1191
- DOI: https://doi.org/10.1090/S0002-9939-08-09603-2
- Published electronically: September 26, 2008
- PDF | Request permission
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 $83$ powers of $2$.References
- P. X. Gallagher, Primes and powers of $2$, Invent. Math. 29 (1975), no. 2, 125–142. MR 379410, DOI 10.1007/BF01390190
- Glyn Harman and Angel V. Kumchev, On sums of squares of primes, Math. Proc. Cambridge Philos. Soc. 140 (2006), no. 1, 1–13. MR 2197572, DOI 10.1017/S0305004105008819
- D. R. Heath-Brown and J.-C. Puchta, Integers represented as a sum of primes and powers of two, Asian J. Math. 6 (2002), no. 3, 535–565. MR 1946346, DOI 10.4310/AJM.2002.v6.n3.a7
- L. K. Hua, Some results in the additive prime number theory, Quart. J. Math. (Oxford), 9(1938), 68-80.
- Angel V. Kumchev, On Weyl sums over primes and almost primes, Michigan Math. J. 54 (2006), no. 2, 243–268. MR 2252758, DOI 10.1307/mmj/1156345592
- Hongze Li, The number of powers of 2 in a representation of large even integers by sums of such powers and of two primes, Acta Arith. 92 (2000), no. 3, 229–237. MR 1752027, DOI 10.4064/aa-92-3-229-237
- Hongze Li, The number of powers of 2 in a representation of large even integers by sums of such powers and of two primes. II, Acta Arith. 96 (2001), no. 4, 369–379. MR 1811879, DOI 10.4064/aa96-4-7
- Hongze Li, Representation of odd integers as the sum of one prime, two squares of primes and powers of 2, Acta Arith. 128 (2007), no. 3, 223–233. MR 2313991, DOI 10.4064/aa128-3-3
- Yu. V. Linnik, Prime numbers and powers of two, Trudy Mat. Inst. Steklov. 38 (1951), 152–169 (Russian). MR 0050618
- Yu. V. Linnik, Addition of prime numbers with powers of one and the same number, Mat. Sbornik N.S. 32(74) (1953), 3–60 (Russian). MR 0059938, DOI 10.1016/0370-1573(77)90003-5
- Jianya Liu, Mingchit Liu, and Tianze Wang, The number of powers of $2$ in a representation of large even integers. II, Sci. China Ser. A 41 (1998), no. 12, 1255–1271. MR 1681935, DOI 10.1007/BF02882266
- Jianya Liu, Ming-Chit Liu, and Tao Zhan, Squares of primes and powers of $2$, Monatsh. Math. 128 (1999), no. 4, 283–313. MR 1726765, DOI 10.1007/s006050050065
- Jianya Liu and Ming-Chit Liu, Representation of even integers as sums of squares of primes and powers of 2, J. Number Theory 83 (2000), no. 2, 202–225. MR 1772613, DOI 10.1006/jnth.1999.2500
- Tao Liu, Representation of odd integers as the sum of one prime, two squares of primes and powers of 2, Acta Arith. 115 (2004), no. 2, 97–118. MR 2099833, DOI 10.4064/aa115-2-1
- Jianya Liu and Guangshi Lü, Four squares of primes and 165 powers of 2, Acta Arith. 114 (2004), no. 1, 55–70. MR 2067872, DOI 10.4064/aa114-1-4
- J. Pintz and I. Z. Ruzsa, On Linnik’s approximation to Goldbach’s problem. I, Acta Arith. 109 (2003), no. 2, 169–194. MR 1980645, DOI 10.4064/aa109-2-6
- J. Pintz, A note on Romanov’s constant, Acta Math. Hungar. 112 (2006), no. 1-2, 1–14. MR 2251126, DOI 10.1007/s10474-006-0060-6
- Xiumin Ren, On exponential sums over primes and application in Waring-Goldbach problem, Sci. China Ser. A 48 (2005), no. 6, 785–797. MR 2158973, DOI 10.1360/03ys0341
- Ming Qiang Wang and Xian Meng Meng, The exceptional set in the two prime squares and a prime problem, Acta Math. Sin. (Engl. Ser.) 22 (2006), no. 5, 1329–1342. MR 2251394, DOI 10.1007/s10114-005-0701-7
- Tianze Wang, On Linnik’s almost Goldbach theorem, Sci. China Ser. A 42 (1999), no. 11, 1155–1172. MR 1749863, DOI 10.1007/BF02875983
- J. Wu, Chen’s double sieve, Goldbach’s conjecture and the twin prime problem, Acta Arith. 114 (2004), no. 3, 215–273. MR 2071082, DOI 10.4064/aa114-3-2
Bibliographic 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
- MR Author ID: 856910
- Received by editor(s): January 30, 2008
- Received by editor(s) in revised form: April 4, 2008
- Published electronically: 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 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 1185-1191
- MSC (2000): Primary 11P32, 11P05, 11N36, 11P55
- DOI: https://doi.org/10.1090/S0002-9939-08-09603-2
- MathSciNet review: 2465639