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By this, I mean, for example, arithmetic progression implied by Riemann zeta function. Are there any resources talking about this topic in general?

Moreover, Weil's theorem says that the zeta function of a variety is rational, making it possible to compute the zeta function. Are there any versions of L-functions easy for computation? Are the values of equivalent importance at every point? Are there any general strategies for computing values of L-function?

Are there any recent papers on the computation of L-functions and arithmetic information implied by values of it?

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Many questions along these lines have appeared on this site already. Search "L-functions". – David Hansen Apr 26 2010 at 23:34
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See also: MO is not a substitute for a graduate course.. – Yemon Choi May 2 2010 at 19:54

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