TY - JOUR
T1 - Unnormalized differences between zeros of L-functions
AU - Ford, Kevin
AU - Zaharescu, Alexandru
N1 - Publisher Copyright:
© 2014 Foundation Compositio Mathematica.
PY - 2015/2/25
Y1 - 2015/2/25
N2 - We 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 ℚ is encoded in the sequences of zeros of other L-functions, not only the one associated to the curve.
AB - We 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 ℚ is encoded in the sequences of zeros of other L-functions, not only the one associated to the curve.
KW - L-functions
KW - Riemann zeta function
KW - distribution of zeros
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U2 - 10.1112/S0010437X14007659
DO - 10.1112/S0010437X14007659
M3 - Article
AN - SCOPUS:84923543578
SN - 0010-437X
VL - 151
SP - 230
EP - 252
JO - Compositio Mathematica
JF - Compositio Mathematica
IS - 2
ER -