Structure of sets with small sumset
Structure theory of set addition, Astérisque, no. 258 (1999), pp. 77-108.
@incollection{AST_1999__258__77_0,
     author = {Bilu, Yuri},
     title = {Structure of sets with small sumset},
     booktitle = {Structure theory of set addition},
     editor = {Deshouilliers Jean-Marc and Landreau Bernard and Yudin Alexander A.},
     series = {Ast\'erisque},
     pages = {77--108},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {258},
     year = {1999},
     mrnumber = {1701189},
     zbl = {0946.11004},
     language = {en},
     url = {http://www.numdam.org/item/AST_1999__258__77_0/}
}
TY  - CHAP
AU  - Bilu, Yuri
TI  - Structure of sets with small sumset
BT  - Structure theory of set addition
AU  - Collectif
ED  - Deshouilliers Jean-Marc
ED  - Landreau Bernard
ED  - Yudin Alexander A.
T3  - Astérisque
PY  - 1999
SP  - 77
EP  - 108
IS  - 258
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_1999__258__77_0/
LA  - en
ID  - AST_1999__258__77_0
ER  - 
%0 Book Section
%A Bilu, Yuri
%T Structure of sets with small sumset
%B Structure theory of set addition
%A Collectif
%E Deshouilliers Jean-Marc
%E Landreau Bernard
%E Yudin Alexander A.
%S Astérisque
%D 1999
%P 77-108
%N 258
%I Société mathématique de France
%U http://www.numdam.org/item/AST_1999__258__77_0/
%G en
%F AST_1999__258__77_0
Bilu, Yuri. Structure of sets with small sumset, dans Structure theory of set addition, Astérisque, no. 258 (1999), pp. 77-108. http://www.numdam.org/item/AST_1999__258__77_0/

[1] Bilu Y., The (α+2β)-inequality on the torus, J. London Math. Soc., to appear. | MR | Zbl

[2] Bilu Y., Lev V. F., Ruzsa I. Z., Rectification principles in additive number theory, Discr. Comput. Geom., 19, 1998, 343-353. | DOI | MR | Zbl

[3] Bombieri E., Vaaler J., On Siegel's Lemma, Inv. Math., 73, 1983, 11-31. | DOI | EuDML | MR | Zbl

[4] Brailovski L. V, Preiman G. A., On a Product of Finite Subsets in a Torsion-Free Group, J. Algebra, 130, 1990, 462-476. | DOI | MR | Zbl

[5] Cassels J. W. S., An Introduction to the Geometry of Numbers, Springer, 1959. | DOI | MR | Zbl

[6] Cauchy A. L., Recherches sur les nombres, J. École Polytech., 9, 1813, 99-116.

[7] Davenport H., On the addition of residue classes, J. London Math. Soc., 10, 1935, 30-32. | DOI | JFM

[8] Davenport H., A historical note, J. London Math. Soc., 22, 1947, 100-101. | DOI | MR | Zbl

[9] Fishburn P. C., On a contribution of Freiman to additive number theory, J. Number Theory, 35, 1990, 325-334. | DOI | MR | Zbl

[10] Freiman G. A., Inverse problems in additive number theory VI., On the addition of finite sets III (Russian), Izv. Vyss. Učebn. Zaved. Matem., no. 3 (28), 1962, 151-157. | MR

[11] Freiman G. A., Inverse problems of additive number theory, VII. On addition of finite sets, IV. The method of trigonometric sums (Russian), Izv. Vyss. Učebn. Zaved. Matem., No 3 (28), 1962, 131-144. | MR | Zbl

[12] Freiman G. A., Foundations of a Structural Theory of Set Addition (Russian), Kazan', 1959 ; English Translation : Translation of Mathematical Monographs 37, Amer. Math. Soc., Providence, 1973. | MR | Zbl

[13] Freiman G. A., What is the structure of K if K+K is small?, Number Theory, New York 1984-1985, Lecture Notes in Math., 1240, Springer, 1987, 109-134 | DOI | MR | Zbl

[14] Freiman G. A., Heppes A., Uhrin B., A lower estimation for the cardinality of finite difference sets in n , Proc. Conf. Number Theory, Budapest 1987, Coll. Math. Soc. J. Bolyai, Budapest, 51, 1989, 125-139. | MR | Zbl

[15] Hamidoune Y. O., On inverse additive problems, Preprint EC95/01, Inst. Blaise Pascal, Paris, January 1995.

[16] Hamidoune Y. O., An Isoperimetric Method in Additive Theory, J. Algebra, 179, 1996, 622-630. | DOI | MR | Zbl

[17] Hamidoune Y. O., Some Results in Additive Number Theory, Rapport ECH197, Univ. Paris VI, 1997. | Zbl

[18] Kemperman I. H. B., On small sumsets in an abelian group, Acta Math., 103, 1960, 63-88. | DOI | MR | Zbl

[19] Kemperman I. H. B., On products of sets in a locally compact group, Fund. Math., 56, 1964, 51-68. | DOI | EuDML | MR | Zbl

[20] Kneser M., Ein Satz über abelschen Gruppen mit Anwendungen auf die Geometrie der Zahlen, Math. Z., 61, 1955, 429-434. | DOI | EuDML | MR | Zbl

[21] Kneser M., Summenmengen in lokalkompakten abelschen Gruppen, Math. Z., 66, 1956, 88-110. | DOI | EuDML | MR | Zbl

[22] Lev V. F., Structure Theorem for Multiple Addition and Frobenius Problem, J. Number Th., 58, 1996, 79-88 | DOI | MR | Zbl

Lev V. F., Structure Theorem for Multiple Addition and Frobenius Problem, J. Number Th., addendum : 65, 1997, 96-100. | DOI | MR | Zbl

[23] Lev V. F., Smeliansky P. Y., On addition of two distinct sets of integers, Acta Arith., 70, 1995, 85-91. | DOI | EuDML | MR | Zbl

[24] Mann H., Addition Theorems : the Addition Theorems of Group Theory and Number Theory, Wiley, New York, 1965. | MR | Zbl

[25] Nathanson M. B., An inverse theorem for sums of sets of lattice points, J. Number Theory, 46, 1994, 29-59. | DOI | MR | Zbl

[26] Nathanson M. B., Additive Number Theory : 2. Inverse Theorems and the Geometry of Sumsets, Graduate Text in Math. 165, Springer, New York, 1996. | DOI | MR | Zbl

[27] Postnikova L. P., Fluctuations in the distribution of fractional parts (Russian), Dokl. Akad. Nauk SSSR, 161, 1965, 1282-1284 ; English Translation : Soviet Math. Dokl., 6, 1965, 597-600. | MR | Zbl

[28] Ruzsa I. Z., Arithmetical progressions and the number of sums, Per. Math. Hung., 25, 1992, 105-111. | DOI | MR | Zbl

[29] Ruzsa I. Z., A concavity property of for the measure of product sets in groups, Fund. Math., 140, 1992, 247-254. | DOI | EuDML | MR | Zbl

[30] Ruzsa I. Z., Generalized arithmetical progressions and sumsets, Acta Math. Hungar., 65 (1994), 379-388. | DOI | MR | Zbl

[31] Ruzsa I. Z., Sums of sets in several dimensions, Combinatorica, 14, 1994, 485-490. | DOI | MR | Zbl

[32] Stanchescu Y., On addition of two distinct sets of integers, Acta Arith., 75, 1996, 191-194. | DOI | EuDML | MR | Zbl

[33] Stanchescu Y., On the structure of sets with small doubling property on the plane (I), Acta Arith., 83, 1998, 127-141. | DOI | EuDML | MR | Zbl

[34] Stanchescu Y., On finite difference sets, Acta Math. Hungar., 79, 1998, 123-138. | DOI | MR | Zbl

[35] Steinig J., On Freiman's theorems concerning the sum of two finite sets of integers, this volume. | Numdam | Zbl

[36] Vosper A. G., The critical pairs of subsets of a group of prime order, J. London Math. Soc., 31, 1956, 200-205, 280-282. | MR | Zbl

[37] Zemor G., Subset sums for binary spaces, Europ. J. Combin., 13, 1992, 221-230. | DOI | MR | Zbl

[38] Zemor G., A generalization to noncommutative groups of a theorem of Mann, Discr. Math., 126, 1994, 365-372. | DOI | MR | Zbl