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· 1996

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Rational points in a family of conics over $\mathbb{F}_2(t)$

math.NT · 2024-12-19 · accept · novelty 7.0

Over F_2(t), the number of parameters y of height 2^M for which the conic x0^2+x0x1+yx1^2=t x2^2 has a rational point is asymptotically c 2^{2M}/M^{1/2}, with an explicit Euler product constant c.

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  • Rational points in a family of conics over $\mathbb{F}_2(t)$ math.NT · 2024-12-19 · accept · none · ref 6

    Over F_2(t), the number of parameters y of height 2^M for which the conic x0^2+x0x1+yx1^2=t x2^2 has a rational point is asymptotically c 2^{2M}/M^{1/2}, with an explicit Euler product constant c.