Complexity and real computation
Complexity and real computation
On Implications between P-NP-Hypotheses: Decision versus Computation in Algebraic Complexity
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Straight-line complexity and integer factorization
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
On the Ultimate Complexity of Factorials
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
On the ultimate complexity of factorials
Theoretical Computer Science
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In this paper, we show several connections between the L- conjecture, proposed by Burgisser [3], and the boundedness theorem for the torsion of elliptic curves. Assuming the L-conjecture, a sharper bound is obtained for the number of torsions over extensions of k on an elliptic curve over a number field k, which improves Masser's result [6]. It is also shown that the Torsion Theorem for elliptic curves [10] follows directly from the WL-conjecture, which is a much weaker version of the L-conjecture. Since the WL-conjecture differs from the trivial lower bound only at the coefficient, this result provides an interesting example where increasing the coefficient in a trivial lower bound of straight-line complexity is difficult and important.