The product of N linear forms in a field of series and the Riemann hypothesis for curves
Colloque de théorie des nombres (Bordeaux, 1969), Bulletin de la Société mathématique de France. Mémoire, no. 25 (1971), pp. 17-27 
@incollection{MSMF_1971__25__17_0,
     author = {Armitage, J. V.},
     title = {The product of $N$ linear forms in a field of series and the {Riemann} hypothesis for curves},
     booktitle = {Colloque de th\'eorie des nombres (Bordeaux, 1969)},
     series = {Bulletin de la Soci\'et\'e math\'ematique de France. M\'emoire},
     pages = {17--27},
     year = {1971},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {25},
     doi = {10.24033/msmf.29},
     mrnumber = {50 #12923},
     zbl = {0221.14017},
     url = {https://www.numdam.org/articles/10.24033/msmf.29/}
}
TY  - CHAP
AU  - Armitage, J. V.
TI  - The product of $N$ linear forms in a field of series and the Riemann hypothesis for curves
BT  - Colloque de théorie des nombres (Bordeaux, 1969)
AU  - Collectif
T3  - Bulletin de la Société mathématique de France. Mémoire
PY  - 1971
SP  - 17
EP  - 27
IS  - 25
PB  - Société mathématique de France
UR  - https://www.numdam.org/articles/10.24033/msmf.29/
DO  - 10.24033/msmf.29
ID  - MSMF_1971__25__17_0
ER  - 
%0 Book Section
%A Armitage, J. V.
%T The product of $N$ linear forms in a field of series and the Riemann hypothesis for curves
%B Colloque de théorie des nombres (Bordeaux, 1969)
%A Collectif
%S Bulletin de la Société mathématique de France. Mémoire
%D 1971
%P 17-27
%N 25
%I Société mathématique de France
%U https://www.numdam.org/articles/10.24033/msmf.29/
%R 10.24033/msmf.29
%F MSMF_1971__25__17_0
Armitage, J. V. The product of $N$ linear forms in a field of series and the Riemann hypothesis for curves, dans Colloque de théorie des nombres (Bordeaux, 1969), Bulletin de la Société mathématique de France. Mémoire, no. 25 (1971), pp. 17-27. doi: 10.24033/msmf.29

[1] J.V. Armitage. On a method of Mordell in the geometry of numbers, Mathematika 2 (1955), 132-140. | Zbl | MR

[2] J.V. Armitage. The product of n linear forms in a field of series, Mathematika 4 (1957), 132-137. | Zbl | MR

[3] J.V. Armitage. Algebraic functions and an analogue of the geometry of numbers : the Riemann-Roch Theorem, Archiv der Mathematik 18 (1967), 383-393. | Zbl | MR

[4] C. Chevalley. L'hypothèse de Riemann pour les corps de fonctions algébriques de caractéristique p, Séminaire Bourbaki 1 (1948/1949), n° 3 and n° 9. | Zbl | Numdam

[5] H. Hasse. Zur Theorie der abstrakten elliptischen Funktionenkörper, J. reine u. angew. Math. 175 (1936), 69-88 and 193-208. | Zbl

[6] K. Mahler. An analogue to Minkowski's geometry of numbers in a field of series, Ann. Math., II Ser. 42 (1941), 481-522. | Zbl | MR | JFM

[7] A. Weil. Sur les courbes algébriques et les variétés qui s'en déduisent, Actualités scientifiques et industrielles, n° 1041, Paris, (1948). | Zbl | MR

[8] A. Weil. Numbers of solutions of equations in finite fields, Bull. Amer. Math. Soc. 55 (1949), 497-508. | Zbl | MR

Cité par Sources :