Inverse theorems and the number of sums and products
Structure theory of set addition, Astérisque, no. 258 (1999), pp. 195-204. 
@incollection{AST_1999__258__195_0,
     author = {Nathanson, Melvyn B. and Tenenbaum, G\'erald},
     title = {Inverse theorems and the number of sums and products},
     booktitle = {Structure theory of set addition},
     editor = {Deshouilliers Jean-Marc and Landreau Bernard and Yudin Alexander A.},
     series = {Ast\'erisque},
     pages = {195--204},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {258},
     year = {1999},
     mrnumber = {1701198},
     zbl = {0947.11008},
     language = {en},
     url = {http://archive.numdam.org/item/AST_1999__258__195_0/}
}
TY  - CHAP
AU  - Nathanson, Melvyn B.
AU  - Tenenbaum, Gérald
TI  - Inverse theorems and the number of sums and products
BT  - Structure theory of set addition
AU  - Collectif
ED  - Deshouilliers Jean-Marc
ED  - Landreau Bernard
ED  - Yudin Alexander A.
T3  - Astérisque
PY  - 1999
SP  - 195
EP  - 204
IS  - 258
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_1999__258__195_0/
LA  - en
ID  - AST_1999__258__195_0
ER  - 
%0 Book Section
%A Nathanson, Melvyn B.
%A Tenenbaum, Gérald
%T Inverse theorems and the number of sums and products
%B Structure theory of set addition
%A Collectif
%E Deshouilliers Jean-Marc
%E Landreau Bernard
%E Yudin Alexander A.
%S Astérisque
%D 1999
%P 195-204
%N 258
%I Société mathématique de France
%U http://archive.numdam.org/item/AST_1999__258__195_0/
%G en
%F AST_1999__258__195_0
Nathanson, Melvyn B.; Tenenbaum, Gérald. Inverse theorems and the number of sums and products, dans Structure theory of set addition, Astérisque, no. 258 (1999), pp. 195-204. http://archive.numdam.org/item/AST_1999__258__195_0/

[1] Barban M. B. and Vehov P. P., Summation of multiplicative functions of polynomials (in Russian), Mat. Zametki, 5(6): 669-680, 1969. English translation: Math. Notes Acad. Sci. USSR, 5, 1969, 400-407. | MR | Zbl

[2] Erdős P., An asymptotic inequality in the theory of numbers (in Russian), Vestnik Leningrad Univ., Serija Mat. Mekh. i Astr., 15(13), 1960, 41-49. | MR | Zbl

[3] Erdős P., Problems and results on combinatorial number theory III, In M. B. Nathanson, editor, Number Theory Day, New York 1976, volume 626 of Lecture Notes in Mathematics, Berlin, Springer-Verlag, 1977, 43-72. | DOI | MR | Zbl

[4] Erdős P. and Szemeredi E., On sums and products of integers, In P. Erdős, L. Alpár, G. Halâsz, and A. Sârkôzy, editors, Studies in Pure Mathematics, To the Memory of Paul Turân, Birkhäuser Verlag, Basel, 1983, 213-218. | DOI | Zbl

[5] Freiman G. A., On the addition of finite sets. I, Izv. Vysh. Zaved. Matematika, 13 (6), 1959, 202-213. | MR | Zbl

[6] Freiman G. A., Inverse problems of additive number theory. VI on the addition of finite sets . III Izv. Vysh. Ucheb. Zaved. Matematika, 28(3), 1962, 151-157. | MR | Zbl

[7] Freiman G. A., Foundations of a Structural Theory of Set Addition, volume 37 of Translations of Mathematical Monographs, American Mathematical Society, Providence, 1973. | MR | Zbl

[8] Hall R. R. and Tenenbaum G., Divisors, Number 90 in Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge, 1988. | MR | Zbl

[9] Lev V. F. and Smeliansky P. Y., On addition of two different sets of integers, Preprint, 1994. | MR

[10] Nathanson M. B., The simplest inverse problems in additive number theory, In A. Pollington and W. Moran, editors, Number Theory with an Emphasis on the Mark off Spectrum, Marcel Dekker, 1993, 191-206. | MR | Zbl

[11] Nathanson M. B., On sums and products of integers, submitted, 1994. | MR | Zbl

[12] Nathanson M. B., Additive Number Theory: 2. Inverse Theorems and the Geometry of Sumsets, Graduate Texts in Mathematics. Springer-Verlag, New York, 1995, to appear. | MR | Zbl

[13] Ruzsa I. Z., Generalized arithmetic progressions and sumsets, to appear. | MR | Zbl

[14] Shiu P., A Brun-Titchmarsh theorem for multiplicative functions, J. reine angew. Math., 313, 1980, 161-170. | EuDML | MR | Zbl

[15] Steinig J., On G. A. Freiman's theorems concerning the sum of two finite sets of integers, In Conference on the Structure Theory of Set Addition, CIRM, Marseille, 1993, 173-186.

[16] Tenenbaum G., Sur la probabilité qu'un entier possède un diviseur dans un intervalle donné, In Séminaire de Théorie des Nombres, Paris 1981-1982, volume 38 of Progress in Math., Birkhäuser, Boston, 1983, 303-312. | EuDML | MR | Zbl

[17] Tenenbaum G., Sur la probabilité qu'un entier possède un diviseur dans un intervalle donné, Compositio Math., 51, 1984, 243-263. | EuDML | Numdam | MR | Zbl

[18] Vinogradov A. I. and Linnik Yu. V., Estimate of the sum of the number of divisors in a short segment of an arithmetic progression, Uspekhi Mat. Nauk (N.S.), 12, 1957, 277-280. | MR | Zbl