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- W2949120033 abstract "We derive strong and effective lower bounds for the class number h(q) of the imaginary quadratic field Q(sqrt{-q}), conditionally subject to the existence of many small (subnormal) gaps between zeros of the L-function associated with a character of the class group associated with this field. In particular, we prove that if the gap between consecutive zeros of the L-function is somewhat smaller than the average for sufficiently many pairs of zeros on the critical line, then h >> sqrt q (log q)^{-A} for some constant A > 0. For the trivial character, the L-function is the Dedekind zeta-function of the number field and so contains the Riemann zeta-function as a factor. Thus, as a corollary to our main result, we prove that this lower bound for h follows from the hypothesis that there are sufficiently many pairs of adjacent zeros of the Riemann zeta-function on the critical line whose spacing is slightly smaller than 1/2 of the average spacing." @default.
- W2949120033 created "2019-06-27" @default.
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- W2949120033 date "2001-11-01" @default.
- W2949120033 modified "2023-09-27" @default.
- W2949120033 title "Spacing of zeros of Hecke L-functions and the class number problem" @default.
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