On the exceptional set of Lagrange’s equation with three prime and one almost–prime variables
- [1] Department of Mathematics Plovdiv University “P. Hilendarski" 24 “Tsar Asen" str. Plovdiv 4000, Bulgaria
Journal de Théorie des Nombres de Bordeaux (2005)
- Volume: 17, Issue: 3, page 925-948
- ISSN: 1246-7405
Access Full Article
topAbstract
topHow to cite
topTolev, Doychin. "On the exceptional set of Lagrange’s equation with three prime and one almost–prime variables." Journal de Théorie des Nombres de Bordeaux 17.3 (2005): 925-948. <http://eudml.org/doc/249469>.
@article{Tolev2005,
abstract = {We consider an approximation to the popular conjecture about representations of integers as sums of four squares of prime numbers.},
affiliation = {Department of Mathematics Plovdiv University “P. Hilendarski" 24 “Tsar Asen" str. Plovdiv 4000, Bulgaria},
author = {Tolev, Doychin},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
number = {3},
pages = {925-948},
publisher = {Université Bordeaux 1},
title = {On the exceptional set of Lagrange’s equation with three prime and one almost–prime variables},
url = {http://eudml.org/doc/249469},
volume = {17},
year = {2005},
}
TY - JOUR
AU - Tolev, Doychin
TI - On the exceptional set of Lagrange’s equation with three prime and one almost–prime variables
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 3
SP - 925
EP - 948
AB - We consider an approximation to the popular conjecture about representations of integers as sums of four squares of prime numbers.
LA - eng
UR - http://eudml.org/doc/249469
ER -
References
top- C. Bauer, M.-C. Liu, T. Zhan, On a sum of three prime squares. J. Number Theory 85 (2000), 336–359. Zbl0961.11034MR1802721
- J. Brüdern, E. Fouvry, Lagrange’s Four Squares Theorem with almost prime variables. J. Reine Angew. Math. 454 (1994), 59–96. Zbl0809.11060MR1288679
- G. Greaves, On the representation of a number in the form where and are odd primes. Acta Arith. 29 (1976), 257–274. Zbl0283.10030MR404182
- H. Halberstam, H.-E. Richert, Sieve methods. Academic Press, 1974. Zbl0298.10026MR424730
- G. H. Hardy, E. M. Wright, An introduction to the theory of numbers. Fifth ed., Oxford Univ. Press, 1979. Zbl0423.10001MR568909
- G. Harman, A. V. Kumchev, On sums of squares of primes. Math. Proc. Cambridge Philos. Soc., to appear. Zbl1114.11079MR2197572
- D.R. Heath-Brown, Cubic forms in ten variables. Proc. London Math. Soc. 47 (1983), 225–257. Zbl0494.10012MR703978
- D.R. Heath-Brown, D.I.Tolev, Lagrange’s four squares theorem with one prime and three almost–prime variables. J. Reine Angew. Math. 558 (2003), 159–224. Zbl1022.11050MR1979185
- L.K. Hua, Some results in the additive prime number theory. Quart. J. Math. Oxford 9 (1938), 68–80. Zbl0018.29404
- L.K. Hua, Introduction to number theory. Springer, 1982. Zbl0483.10001MR665428
- L.K. Hua, Additive theory of prime numbers. American Mathematical Society, Providence, 1965. Zbl0192.39304MR194404
- H. Iwaniec, Rosser’s sieve. Acta Arith. 36 (1980), 171–202. Zbl0435.10029MR581917
- H. Iwaniec, A new form of the error term in the linear sieve. Acta Arith. 37 (1980), 307–320. Zbl0444.10038MR598883
- H.D. Kloosterman, On the representation of numbers in the form . Acta Math. 49 (1926), 407–464. Zbl53.0155.01
- J. Liu, On Lagrange’s theorem with prime variables. Quart. J. Math. Oxford, 54 (2003), 453–462. Zbl1080.11071MR2031178
- J. Liu, M.-C. Liu, The exceptional set in the four prime squares problem. Illinois J. Math. 44 (2000), 272–293. Zbl0942.11044MR1775322
- J.Liu, T. D. Wooley, G. Yu, The quadratic Waring–Goldbach problem. J. Number Theory, 107 (2004), 298–321. Zbl1056.11055MR2072391
- V.A. Plaksin, An asymptotic formula for the number of solutions of a nonlinear equation for prime numbers. Math. USSR Izv. 18 (1982), 275–348. Zbl0482.10045
- P. Shields, Some applications of the sieve methods in number theory. Thesis, University of Wales 1979.
- D.I. Tolev, Additive problems with prime numbers of special type. Acta Arith. 96, (2000), 53–88. Zbl0972.11096MR1812750
- D.I. Tolev, Lagrange’s four squares theorem with variables of special type. Proceedings of the Session in analytic number theory and Diophantine equations, Bonner Math. Schriften, Bonn, 360 (2003). Zbl1060.11061MR2075638
- T.D. Wooley, Slim exceptional sets for sums of four squares, Proc. London Math. Soc. (3), 85 (2002), 1–21. Zbl1039.11066MR1901366
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.