Unnormalized differences between zeros of L-functions

Author:

Ford Kevin,Zaharescu Alexandru

Abstract

AbstractWe study a subtle inequity in the distribution of unnormalized differences between imaginary parts of zeros of the Riemann zeta function, which was observed by a number of authors. We establish a precise measure which explains the phenomenon, 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 $\mathbb{Q}$ is encoded in the sequences of zeros of other$L$-functions, not only the one associated to the curve.

Publisher

Wiley

Subject

Algebra and Number Theory

Reference41 articles.

1. Le spectre résiduel de ${\rm GL}(n)$

2. Statistical theory of the energy levels of complex systems, I, II, III;Dyson;J. Math. Phys.,1962

3. Autocorrelation of ratios of $L$-functions

4. On the distribution of spacings between zeros of the zeta function

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