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In algebraic number theory, a supersingular prime is a prime number with a certain relationship to a given elliptic curve. If the curve ''E'' defined over the rational numbers, then a prime ''p'' is supersingular for ''E'' if the reduction of ''E'' modulo ''p'' is a supersingular elliptic curve over the residue field Fp. showed that any elliptic curve over the rational numbers has infinitely many supersingular primes. However, the set of supersingular primes has asymptotic density zero. conjectured that the number of supersingular primes less than a bound ''X'' is within a constant multiple of , using heuristics involving the distribution of eigenvalues of the Frobenius endomorphism. , this conjecture is open. More generally, if ''K'' is any global field—i.e., a finite extension either of Q or of Fp(''t'')—and ''A'' is an abelian variety defined over ''K'', then a supersingular prime for ''A'' is a finite place of ''K'' such that the reduction of ''A'' modulo is a supersingular abelian variety. == References == * * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Supersingular prime (for an elliptic curve)」の詳細全文を読む スポンサード リンク
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