17 research outputs found
Features of Buildings Made of Soil Materials in Seismic Areas
The article discusses the technology of producing thermoelectric materials under inert gas pressure, which makes it possible to provide reproducible results from melting to melting and to synthesize sufficiently large amounts of a working substance
Toward verification of the Riemann hypothesis: Application of the Li criterion
We substantially apply the Li criterion for the Riemann hypothesis to hold.
Based upon a series representation for the sequence \{\lambda_k\}, which are
certain logarithmic derivatives of the Riemann xi function evaluated at unity,
we determine new bounds for relevant Riemann zeta function sums and the
sequence itself. We find that the Riemann hypothesis holds if certain
conjectured properties of a sequence \eta_j are valid. The constants \eta_j
enter the Laurent expansion of the logarithmic derivative of the zeta function
about s=1 and appear to have remarkable characteristics. {\em On our
conjecture}, not only does the Riemann hypothesis follow, but an inequality
governing the values \lambda_n and inequalities for the sums of reciprocal
powers of the nontrivial zeros of the zeta function.Comment: to appear in Math. Physics, Analysis and Geometry; 1 figur