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  Numerical investigations related to the L-series of certain elliptic curves.

Zagier, D., & Kramarz, G. (1987). Numerical investigations related to the L-series of certain elliptic curves. The Journal of the Indian Mathematical Society. New Series, 52, 51-69.

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Datensatz-Permalink: https://hdl.handle.net/21.11116/0000-0004-395B-7 Versions-Permalink: https://hdl.handle.net/21.11116/0000-0004-395C-6
Genre: Zeitschriftenartikel

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 Urheber:
Zagier, Don1, Autor           
Kramarz, G.2, Autor
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              
2Max Planck Society, ou_persistent13              

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Schlagwörter: -
 Zusammenfassung: As the title indicates, the authors make computations around the Birch and Swinnerton-Dyer conjecture for the family x\sp 3+y\sp 3=m, m\in \bbfN, in the range m≤ 70000. They compute approximations of L(1) and L'(1). They show that the density of curves with a zero of order ≥ 2 (resp. ≥ 3) does not seem to be 0 as expected by the experts. Using these approximations as well as the Birch and Swinnerton-Dyer conjecture, the authors compute the order of the Tate-Shafarevich group. The results are presented graphically. Finally, a tentative analogue of the Cohen-Lenstra heuristic is presented and discussed but, as the authors observe the recipe does not seem to work in this case.

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 Datum: 1987
 Publikationsstatus: Erschienen
 Seiten: -
 Ort, Verlag, Ausgabe: -
 Inhaltsverzeichnis: -
 Art der Begutachtung: -
 Identifikatoren: eDoc: 744947
Anderer: 111
 Art des Abschluß: -

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Titel: The Journal of the Indian Mathematical Society. New Series
Genre der Quelle: Zeitschrift
 Urheber:
Affiliations:
Ort, Verlag, Ausgabe: Indian Mathematical Society c/o Department of Mathematics, University of Pune, Pune, Maharashtra, India
Seiten: - Band / Heft: 52 Artikelnummer: - Start- / Endseite: 51 - 69 Identifikator: ISSN: 0019-5839