The highest lowest zero of general L-functions
| Autor: | Bober, Jonathan, Conrey, J. Brian, Farmer, David W., Fujii, Akio, Koutsoliotas, Sally, Lemurell, Stefan, Rubinstein, Michael, Yoshida, Hiroyuki |
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| Rok vydání: | 2012 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Stephen D. Miller showed that, assuming the generalized Riemann Hypothesis, every entire $L$-function of real archimedian type has a zero in the interval $\frac12+i t$ with $-t_0 < t < t_0$, where $t_0\approx 14.13$ corresponds to the first zero of the Riemann zeta function. We give an example of a self-dual degree-4 $L$-function whose first positive imaginary zero is at $t_1\approx 14.496$. In particular, Miller's result does not hold for general $L$-functions. We show that all $L$-functions satisfying some additional (conjecturally true) conditions have a zero in the interval $(-t_2,t_2)$ with $t_2\approx 22.661$. Comment: Added higher precision values for coefficients. Final version, to appear in JNT |
| Databáze: | arXiv |
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