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Article
Zeta Matrices of Elliptic Curves
Journal of Number Theory
  • Goro Kato, California Polytechnic State University, San Luis Obispo
  • Saul Lubkin, University of Rochester
Publication Date
12-1-1982
Abstract
Let O=limnZ/pnZ, , let A=O[g2,g3] Δ, where g2 and g3 are coefficients of the elliptic curve: Y2 = 4X3 − g2X − g3 over a finite field and Δ = g23 − 27g32 and let B=A[X,Y]/(Y2-4X3+g2X+g3). Then the p-adic cohomology theory will be applied to compute explicitly the zeta matrices of the elliptic curves, induced by the pth power map on the free AzQ -module H1(X, AzQ). Main results are; Theorem 1.1: X2 dY and Y dX are basis elements for H1(X, IA(X)zQ); Theorem 1.2: Y dX, X2 dY, Y−1 dX, Y−2 dX and XY−2 dX are basis elements for H1(X – (Y=0) IA(X)zQ), where X is a lifting of X, and all the necessary recursive formulas for this explicit computation are given.
Disciplines
Citation Information
Goro Kato and Saul Lubkin. "Zeta Matrices of Elliptic Curves" Journal of Number Theory Vol. 15 Iss. 3 (1982) p. 318 - 330
Available at: http://works.bepress.com/gkato/12/