Exact m-covers and the linear form s = 1 k x s / n s

Zhi-Wei Sun

Acta Arithmetica (1997)

  • Volume: 81, Issue: 2, page 175-198
  • ISSN: 0065-1036

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Zhi-Wei Sun. "Exact m-covers and the linear form $∑^k_{s=1} x_s/n_s$." Acta Arithmetica 81.2 (1997): 175-198. <http://eudml.org/doc/207060>.

@article{Zhi1997,
author = {Zhi-Wei Sun},
journal = {Acta Arithmetica},
keywords = {linear form; covering},
language = {eng},
number = {2},
pages = {175-198},
title = {Exact m-covers and the linear form $∑^k_\{s=1\} x_s/n_s$},
url = {http://eudml.org/doc/207060},
volume = {81},
year = {1997},
}

TY - JOUR
AU - Zhi-Wei Sun
TI - Exact m-covers and the linear form $∑^k_{s=1} x_s/n_s$
JO - Acta Arithmetica
PY - 1997
VL - 81
IS - 2
SP - 175
EP - 198
LA - eng
KW - linear form; covering
UR - http://eudml.org/doc/207060
ER -

References

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  1. [E] P. Erdős, On integers of the form 2 k + p and some related problems, Summa Brasil. Math. 2 (1950), 113-123. MR 13, 437. 
  2. [GLS] A. Granville, S.-G. Li and Q. Sun, On the number of solutions of the equation i = 1 n x i / d i 0 ( m o d 1 ) , and of diagonal equations in finite fields, J. Sichuan Univ. (Nat. Sci. Ed.) 32 (3) (1995), 243-248. 
  3. [Gu] R. K. Guy, Unsolved Problems in Number Theory, 2nd ed., Springer, New York, 1994, Sections F13 and F14. 
  4. [LN] R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia Math. Appl., 20, Addison-Wesley, 1983, 291-293. MR 86c:11106. 
  5. [P] Š. Porubský, On m times covering systems of congruences, Acta Arith. 29 (1976), 159-169. MR 53#2884. Zbl0282.10033
  6. [Sm] C. Small, Diagonal equations over large finite fields, Canad. J. Math. 36 (1984), 249-262. MR 86e:11094. 
  7. [SW] Q. Sun and D.-Q. Wan, On the Diophantine equation i = 1 n x i / d i 0 ( m o d 1 ) , Proc. Amer. Math. Soc. 112 (1991), 25-29. MR 91h:11017. 
  8. [SWM] Q. Sun, D.-Q. Wan and D.-G. Ma, On the equation i = 1 n y i / d i 0 ( m o d 1 ) , J. Sichuan Univ. (Nat. Sci. Ed.) 23 (4) (1986), 25-30. MR 88e:11121. 
  9. [Su1] Z. W. Sun, A necessary and sufficient condition for two linear diophantine equations to have a common solution, J. Nanjing Univ. (Nat. Sci. Ed.) 25 (1) (1989), 10-17. MR 90i:11026. 
  10. [Su2] Z. W. Sun, On exactly m times covers, Israel J. Math. 77 (1992), 345-348. MR 93k : 11007. Zbl0768.11001
  11. [Su3] Z. W. Sun, Covering the integers by arithmetic sequences, Acta Arith. 72 (1995), 109-129. Zbl0841.11011
  12. [Su4] Z. W. Sun, Covering the integers by arithmetic sequences II, Trans. Amer. Math. Soc. 348 (1996), 4279-4320. Zbl0884.11013

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