摘要
Let ∞ be a fixed place of a global function field k. Let E be an elliptic curve defined over k which has split multiplicative reduction at ∞ and fix a modular parametrization Φ E :X 0 (Tsh{cyrillic})→E. Let P 1 ,...,P r ∈E(k{topbar}) be Heegner points associated to the rings of integers of distinct quadratic "imaginary" fields K 1 ,...,K r over (k,∞). We prove that if the "prime-to-2. p" part of the ideal class numbers of ring of integers of K 1 ,...,K r are larger than a constant C=C(E,Φ E ) depending only on E and Φ E , then the points P 1 ,...,P r are independent in E(k{topbar})/Etors. Moreover, when k is rational, we show that there are infinitely many imaginary quadratic fields for which the prime-to-2. p part of the class numbers are larger than C. © 2010 Elsevier Inc.