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- W2000346538 abstract "An integern is congruent if there is a triangle with rational sides whose area isn. In the 1980s Tunnell gave an algorithm to test congruence which relied on counting integral points on the ellipsoids 2x 2 +y 2 + 8z 2 =n and 2x 2 +y 2 + 32z 2 =n. The correctness of this algorithm is conditional on the conjecture of Birch and Swinnerton-Dyer. The known methods for testing Tunnell’s criterion useO(n) operations. In this paper we give several methods with smaller exponents, including a randomized algorithm using timen 11/2+o(1) and spacen o(1) and a deterministic algorithm using space and timen 1/2+o(1)." @default.
- W2000346538 created "2016-06-24" @default.
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- W2000346538 date "2007-10-01" @default.
- W2000346538 modified "2023-09-25" @default.
- W2000346538 title "Efficient verification of Tunnell’s criterion" @default.
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- W2000346538 doi "https://doi.org/10.1007/bf03167537" @default.
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