@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, in Structure theory of set addition, Astérisque, no. 258 (1999), pp. 195-204. http://archive.numdam.org/item/AST_1999__258__195_0/
[1] 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
and ,[2] 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] 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] On sums and products of integers, In , , , and , editors, Studies in Pure Mathematics, To the Memory of Paul Turân, Birkhäuser Verlag, Basel, 1983, 213-218. | DOI | Zbl
and ,[5] On the addition of finite sets. I, Izv. Vysh. Zaved. Matematika, 13 (6), 1959, 202-213. | MR | Zbl
,[6] 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] Foundations of a Structural Theory of Set Addition, volume 37 of Translations of Mathematical Monographs, American Mathematical Society, Providence, 1973. | MR | Zbl
,[8] Divisors, Number 90 in Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge, 1988. | MR | Zbl
and ,[9] On addition of two different sets of integers, Preprint, 1994. | MR
and ,[10] 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] On sums and products of integers, submitted, 1994. | MR | Zbl
,[12] 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] Generalized arithmetic progressions and sumsets, to appear. | MR | Zbl
,[14] A Brun-Titchmarsh theorem for multiplicative functions, J. reine angew. Math., 313, 1980, 161-170. | EuDML | MR | Zbl
,[15] 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] 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] Sur la probabilité qu'un entier possède un diviseur dans un intervalle donné, Compositio Math., 51, 1984, 243-263. | EuDML | Numdam | MR | Zbl
,[18] 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
and ,