The Linear Independence hypothesis (LI), which states roughly that theimaginary parts of the critical zeros of Dirichlet L-functions are linearlyindependent over the rationals, is known to have interesting consequences inthe study of prime number races, as was pointed out by Rubinstein and Sarnak.In this paper, we prove that a function field analogue of LI holds genericallywithin certain families of elliptic curve L-functions and their symmetricpowers. More precisely, for certain algebro-geometric families of ellipticcurves defined over the function field of a fixed curve over a finite field, wegive strong quantitative bounds for the number of elements in the family forwhich the relevant L-functions have their zeros as linearly independent overthe rationals as possible.
展开▼
