... Proof. After Lemma 3, it only remains to show that we can take d2 By Theorem 2, it is enough ... more ... Proof. After Lemma 3, it only remains to show that we can take d2 By Theorem 2, it is enough to prove the conjecture when MH is non-zero and attained. Suppose then that L1L2L3 attains its homogeneous Page 12. 36 BJ BIRCH and HPF SWINNERTON-DYER ...
... g ≥ 4 and LE(s) has zero at s = 1 of order ≥ 2. Thus if the conjecture of Birch and Swinnerto... more ... g ≥ 4 and LE(s) has zero at s = 1 of order ≥ 2. Thus if the conjecture of Birch and Swinnerton-Dyer were true, the theorem and class number formula for quadratic fields would give h(−d) > C · log(d) · exp exp(−42 √ (log log d)), C an effective constant, which would solve ...
ELLIPTIC CURVES AND MODULAR FUNCTIONS ~by HPF SWINNERTON-DYER and BJ BIRCH CONTENTS 0~ Introducti... more ELLIPTIC CURVES AND MODULAR FUNCTIONS ~by HPF SWINNERTON-DYER and BJ BIRCH CONTENTS 0~ Introduction i. The zeta-function of an elliptic curve 2. Mellin transforms and Weil'stheorem 3. The theorems of Eichler and Shimura 4. Cusp forms of weight 2 ...
... Proof. After Lemma 3, it only remains to show that we can take d2 By Theorem 2, it is enough ... more ... Proof. After Lemma 3, it only remains to show that we can take d2 By Theorem 2, it is enough to prove the conjecture when MH is non-zero and attained. Suppose then that L1L2L3 attains its homogeneous Page 12. 36 BJ BIRCH and HPF SWINNERTON-DYER ...
... g ≥ 4 and LE(s) has zero at s = 1 of order ≥ 2. Thus if the conjecture of Birch and Swinnerto... more ... g ≥ 4 and LE(s) has zero at s = 1 of order ≥ 2. Thus if the conjecture of Birch and Swinnerton-Dyer were true, the theorem and class number formula for quadratic fields would give h(−d) > C · log(d) · exp exp(−42 √ (log log d)), C an effective constant, which would solve ...
ELLIPTIC CURVES AND MODULAR FUNCTIONS ~by HPF SWINNERTON-DYER and BJ BIRCH CONTENTS 0~ Introducti... more ELLIPTIC CURVES AND MODULAR FUNCTIONS ~by HPF SWINNERTON-DYER and BJ BIRCH CONTENTS 0~ Introduction i. The zeta-function of an elliptic curve 2. Mellin transforms and Weil'stheorem 3. The theorems of Eichler and Shimura 4. Cusp forms of weight 2 ...
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