# Numbers representable by five prime squares with primes in an arithmetic progression

Acta Arithmetica (1999)

- Volume: 90, Issue: 3, page 217-244
- ISSN: 0065-1036

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topYonghui Wang. "Numbers representable by five prime squares with primes in an arithmetic progression." Acta Arithmetica 90.3 (1999): 217-244. <http://eudml.org/doc/207325>.

@article{YonghuiWang1999,

author = {Yonghui Wang},

journal = {Acta Arithmetica},

keywords = {representations by prime squares; singular series; arithmetic progressions},

language = {eng},

number = {3},

pages = {217-244},

title = {Numbers representable by five prime squares with primes in an arithmetic progression},

url = {http://eudml.org/doc/207325},

volume = {90},

year = {1999},

}

TY - JOUR

AU - Yonghui Wang

TI - Numbers representable by five prime squares with primes in an arithmetic progression

JO - Acta Arithmetica

PY - 1999

VL - 90

IS - 3

SP - 217

EP - 244

LA - eng

KW - representations by prime squares; singular series; arithmetic progressions

UR - http://eudml.org/doc/207325

ER -

## References

top- [1] H. Davenport, Multiplicative Number Theory, 2nd ed., Springer, 1980. Zbl0453.10002
- [2] P. X. Gallagher, A large sieve density estimates near σ = 1, Invent. Math. 11 (1970), 329-339. Zbl0219.10048
- [3] L. K. Hua, Additive Theory of Prime Numbers, Transl. Math. Monographs 13, Amer. Math. Soc., 1965. Zbl0192.39304
- [4] J. Y. Liu and T. Zhan, The ternary Goldbach problem in arithmetic progressions, Acta Arith. 82 (1997), 197-227. Zbl0889.11035
- [5] M. C. Liu and K. M. Tsang, Small prime solutions of linear equations, in: Théorie des Nombres, de Gruyter, 1989, 595-624.
- [6] M. C. Liu and K. M. Tsang, Small prime solutions of some additive equations, Monatsh. Math. 111 (1991), 147-169. Zbl0719.11064
- [7] M. C. Liu and T. Zhan, The Goldbach problem with primes in arithmetic progressions, in: Analytic Number Theory, Y. Motohashi (ed.), London Math. Soc. Lecture Note Ser. 247, Cambridge Univ. Press, 1997, 227-251. Zbl0913.11043
- [8] H. L. Montgomery and R. C. Vaughan, The exceptional set of Goldbach's problem, Acta Arith. 27 (1975), 353-370. Zbl0301.10043
- [9] R. C. Vaughan, The Hardy-Littlewood Method, Cambridge Univ. Press, 1981. Zbl0455.10034
- [10] I. M. Vinogradov, Elements of Number Theory, Dover, New York, 1954. Zbl0057.28201
- [11] Y. H. Wang, Some exponential sums over primes in an arithmetic progression, Shanda Xuebao, to appear (in Chinese).

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