ar X iv : m at h - ph / 0 50 70 42 v 1 1 7 Ju l 2 00 5 Polygamma theory , the Li / Keiper constants , and
نویسنده
چکیده
The Riemann hypothesis is equivalent to the Li criterion governing a sequence of real constants {λk}k=1, that are certain logarithmic derivatives of the Riemann xi function evaluated at unity. We investigate a related set of constants cn, n = 1, 2, . . ., showing in detail that the leading behaviour (1/2) ln n of λn/n is absent in cn. Additional results are presented, including a novel explicit representation of cn in terms of the Stieltjes constants γj . We conjecture as to the large-n behaviour of cn. Should this conjecture hold, validity of the Riemann hypothesis would follow.
منابع مشابه
ar X iv : m at h - ph / 0 60 70 40 v 1 2 0 Ju l 2 00 6 Invariant Form of BK - factorization and its Applications
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