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On a Fermat equation arising in the arithmetic theory of functions fields. (English) Zbl 0494.12008


MSC:

11R58 Arithmetic theory of algebraic function fields
11T22 Cyclotomy
11D41 Higher degree equations; Fermat’s equation
14L05 Formal groups, \(p\)-divisible groups
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References:

[1] Carlitz, L.: A class of polynomials. Trans. Am. Math. Soc.43, 168-182 (1938) · JFM 64.0093.01 · doi:10.1090/S0002-9947-1938-1501937-X
[2] Drinfeld, V.G.: Elliptic modules. Math. USSR Sb.23, 561-592 (1974) · Zbl 0321.14014 · doi:10.1070/SM1974v023n04ABEH001731
[3] Drinfeld, V.G.: Elliptic modules. II. Math. USSR-Sb.37, 159-170 (1977) · Zbl 0386.20022 · doi:10.1070/SM1977v031n02ABEH002296
[4] Galovich, S., Rosen, M.: The class number of cyclotomic function fields. J. Number Theory13, 363-376 (1981) · Zbl 0473.12014 · doi:10.1016/0022-314X(81)90021-4
[5] Goss, D.: The algebraist’s upper half-plane. Bull. A.M.S.2, 391-415 (1980) · Zbl 0433.14017 · doi:10.1090/S0273-0979-1980-14751-5
[6] Goss, D.:v-adic zeta functions,L-series and measures for function fields. Invent. Math.55, 107-119 (1979) · Zbl 0413.12008 · doi:10.1007/BF01390084
[7] Goss, D.: Kummer and Herbrand criterion in the theory of function fields. Duke J. Math.49, 377-384 (1982) · Zbl 0485.12010 · doi:10.1215/S0012-7094-82-04923-7
[8] Goss, D.: von-Staudt forF q [T]. Duke Math. J.45, 885-910 (1978) · Zbl 0404.12013 · doi:10.1215/S0012-7094-78-04541-6
[9] Goss, D.: Modular forms forF r [T]. Crelle’s J.31, 16-39 (1980) · Zbl 0422.10021
[10] Goss, D.: The arithmetic of function fields. Seminaire de Theorie des Nombres, Bordeaux, expose No. 32, 1980-81
[11] Goss, D.: The arithmetic of function fields. 2. The ?cyclotomic? theory. J. Algebra (to appear) · Zbl 0516.12010
[12] Goss, B.: The annihilation of divisor classes in Abelian extensions of the rational function field. Seminaire de Theorie des Nombres, Bordeaux expose No. 3, 1980-81
[13] Hayes, D.: Explicit class field theory for rational function fields. Trans. A.M.S.189, 77-91 (1974) · Zbl 0292.12018 · doi:10.1090/S0002-9947-1974-0330106-6
[14] Hayes, D.: Analytic class number formulas in function fields. Invent. Math.65, 49-69 (1981) · Zbl 0491.12014 · doi:10.1007/BF01389294
[15] Thomas, E.: On the zeta function for function fields overE p (to appear)
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