On the exceptional set of Lagrange’s equation with three prime and one almost–prime variables

Doychin Tolev[1]

  • [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

Abstract

top
We consider an approximation to the popular conjecture about representations of integers as sums of four squares of prime numbers.

How to cite

top

Tolev, 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
  1. C. Bauer, M.-C. Liu, T. Zhan, On a sum of three prime squares. J. Number Theory 85 (2000), 336–359. Zbl0961.11034MR1802721
  2. J. Brüdern, E. Fouvry, Lagrange’s Four Squares Theorem with almost prime variables. J. Reine Angew. Math. 454 (1994), 59–96. Zbl0809.11060MR1288679
  3. G. Greaves, On the representation of a number in the form x 2 + y 2 + p 2 + q 2 where p and q are odd primes. Acta Arith. 29 (1976), 257–274. Zbl0283.10030MR404182
  4. H. Halberstam, H.-E. Richert, Sieve methods. Academic Press, 1974. Zbl0298.10026MR424730
  5. G. H. Hardy, E. M. Wright, An introduction to the theory of numbers. Fifth ed., Oxford Univ. Press, 1979. Zbl0423.10001MR568909
  6. G. Harman, A. V. Kumchev, On sums of squares of primes. Math. Proc. Cambridge Philos. Soc., to appear. Zbl1114.11079MR2197572
  7. D.R. Heath-Brown, Cubic forms in ten variables. Proc. London Math. Soc. 47 (1983), 225–257. Zbl0494.10012MR703978
  8. 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
  9. L.K. Hua, Some results in the additive prime number theory. Quart. J. Math. Oxford 9 (1938), 68–80. Zbl0018.29404
  10. L.K. Hua, Introduction to number theory. Springer, 1982. Zbl0483.10001MR665428
  11. L.K. Hua, Additive theory of prime numbers. American Mathematical Society, Providence, 1965. Zbl0192.39304MR194404
  12. H. Iwaniec, Rosser’s sieve. Acta Arith. 36 (1980), 171–202. Zbl0435.10029MR581917
  13. H. Iwaniec, A new form of the error term in the linear sieve. Acta Arith. 37 (1980), 307–320. Zbl0444.10038MR598883
  14. H.D. Kloosterman, On the representation of numbers in the form a x 2 + b y 2 + c z 2 + d t 2 . Acta Math. 49 (1926), 407–464. Zbl53.0155.01
  15. J. Liu, On Lagrange’s theorem with prime variables. Quart. J. Math. Oxford, 54 (2003), 453–462. Zbl1080.11071MR2031178
  16. J. Liu, M.-C. Liu, The exceptional set in the four prime squares problem. Illinois J. Math. 44 (2000), 272–293. Zbl0942.11044MR1775322
  17. J.Liu, T. D. Wooley, G. Yu, The quadratic Waring–Goldbach problem. J. Number Theory, 107 (2004), 298–321. Zbl1056.11055MR2072391
  18. 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
  19. P. Shields, Some applications of the sieve methods in number theory. Thesis, University of Wales 1979. 
  20. D.I. Tolev, Additive problems with prime numbers of special type. Acta Arith. 96, (2000), 53–88. Zbl0972.11096MR1812750
  21. 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
  22. T.D. Wooley, Slim exceptional sets for sums of four squares, Proc. London Math. Soc. (3), 85 (2002), 1–21. Zbl1039.11066MR1901366

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.