zbMATH — the first resource for mathematics

On polynomials and exponential polynomials in several complex variables. (English) Zbl 0436.32005

32A30 Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30-XX)
32A05 Power series, series of functions of several complex variables
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
Full Text: DOI EuDML
[1] Brownawell, W.D., Masset, D.W.: Multiplicity estimates for analytic functions I. J. reine angew. Math.314, 200-216 (1980) · Zbl 0417.10027 · doi:10.1515/crll.1980.314.200
[2] Brownawell, W.D., Masser, D.W.: Multiplicity estimates for analytic functions II. Duke Math. J.47, 273-295 (1980) · Zbl 0461.10027 · doi:10.1215/S0012-7094-80-04718-3
[3] Brownawell, W.D.: On the orders of zeros of certain functions. Mém. Soc. Math. France2, 5-20 (1980) · Zbl 0467.10024
[4] Chudnovsky, G.V.: A mutual transcendence measure for some classes of numbers. Dokl. Akad. Nauk SSSR218, 771-774 (1974); Soviet Math. Dokl.15, 1424-1428 (1974)
[5] Chudnovsky, G.V.: The degree of hypersurfaces containing lattices in ? n I. Planar case (unpublished)
[6] Gröbner, W.: Moderne algebraische Geometrie ? die idealtheoretischen Grundlagen. Wien. Innsbruck: Springer-Verlag 1949 · Zbl 0033.12706
[7] Masser, D.W., Wüstholz, G.: Zero estimates on group varieties · Zbl 0467.10025
[8] Nesterenko, J.V.: Estimates for the orders of zeroes of functions of a certain class and their applications in the theory of transcendental numbers. Izv. Akad. Nauk USSR, Ser. Mat.41, 253-284 (1977); Math. USSR Izv.11, 239-270 (1977) · Zbl 0354.10026
[9] Tijdeman, R.: On the number of zeroes of general exponential polynomials. Indagationes Math.33, 1-7 (1971) · Zbl 0211.09201 · doi:10.1016/S1385-7258(71)80003-3
[10] Tijdeman, R.: An auxiliary result in the theory of transcendental numbers. J. Number Theory5, 80-94 (1973) · Zbl 0254.10027 · doi:10.1016/0022-314X(73)90060-7
[11] Waldschmidt, M.: Nombres transcendants et groupes algébriques. Astérisque69-70 (1979)
[12] Waldschmidt, M.: Transcendence methods. Queen’s Papers in Pure and Applied Mathematics No. 52, Kingston, Ontario 1979
[13] Waldschmidt, M.: Transcendance et exponentielles en plusieurs variables. Invent. math.63, 97-127 (1981) · Zbl 0454.10020 · doi:10.1007/BF01389195
[14] Zariski, O., Samuel, P.: Commutative algebra Vols I, II. New York: Springer-Verlag 1968
[15] Cohen, I.S.: On the structure and ideal theory of complete local rings. Trans. Amer. Math. Soc.59, 54-106 (1946) · Zbl 0060.07001 · doi:10.1090/S0002-9947-1946-0016094-3
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.