Marco’s Repulsion Phenomenon between Zeros of L-functions
نویسندگان
چکیده
We study a subtle inequity in the distribution of differences between imaginary parts of zeros of the Riemann zeta function. We establish a precise measure which explains the phenomenon, first observed by R. P. Marco, that the location of each Riemann zero is encoded in the distribution of large Riemann zeros. We also extend these results to zeros of more general L-functions. In particular, we show how the rank of an elliptic curve over Q is encoded in the sequences of zeros of other L−functions, not only the one associated to the curve.
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