An elementary inequality
M. Marjanović (1964)
Matematički Vesnik
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M. Marjanović (1964)
Matematički Vesnik
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Pambuccian, Victor (2008)
Beiträge zur Algebra und Geometrie
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Žarko Mijajlović (1977)
Publications de l'Institut Mathématique
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Michael Stoll (2001)
Acta Arithmetica
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Stein, William A. (2007)
Documenta Mathematica
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John Tate (1964-1966)
Séminaire Bourbaki
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Michael J. Razar (1977)
Compositio Mathematica
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Barry Mazur (1977)
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Massimo Bertolini (1997)
Collectanea Mathematica
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Ki-Seng Tan (1995)
Annales de l'institut Fourier
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In this paper, we generalize the context of the Mazur-Tate conjecture and sharpen, in a certain way, the statement of the conjecture. Our main result will be to establish the truth of a part of these new sharpened conjectures, provided that one assume the truth of the classical Birch and Swinnerton-Dyer conjectures. This is particularly striking in the function field case, where these results can be viewed as being a refinement of the earlier work of Tate and Milne.