科研之友
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摘要
Let L(s,chi) be a fixed Dirichlet L-function. Given a vertical arithmetic progression of T points on the line Rs = 1/2, we show that at least cT/log T of them are not zeros of L(s,chi) (for some positive constant c). This result provides some theoretical evidence towards the conjecture that all nonnegative ordinates of zeros of Dirichlet L-functions are linearly independent over the rationals. We also establish an upper bound (depending upon the progression) for the first member of the arithmetic progression that is not a zero of L(s,chi).
- 出版日期2013-6
