Special values of L-series attached to two families of CM elliptic curves

【摘要】 <正> Consider two families of elliptic curves y2=x3-D1x and y2=x3-2433D22 over fields and respectively. Formulae expressed by Weierstrass (?)functions are given for special values of Hecke L-se-ries attached to such elliptic curves. The lower bounds of 2-adic and 3-adic valuations of these values of Hecke L-series as well as criteria for reaching these bounds are obtained. These results are consistent with the predictions of the conjecture of Birch and Swinnerton-Dyer; and some results in recent literature for more special case and for 2-adic valuation are also developed.更多还原

【Abstract】 Consider two families of elliptic curves y2=x3-D1x and y2=x3-2433D22 over fields and respectively. Formulae expressed by Weierstrass (?)functions are given for special values of Hecke L-se-ries attached to such elliptic curves. The lower bounds of 2-adic and 3-adic valuations of these values of Hecke L-series as well as criteria for reaching these bounds are obtained. These results are consistent with the predictions of the conjecture of Birch and Swinnerton-Dyer; and some results in recent literature for more special case and for 2-adic valuation are also developed.更多还原