3,912 research outputs found
On the large values of the Riemann zeta-function on short segments of the critical line
In this paper, we obtain a series of new conditional lower bounds for the
modulus and the argument of the Riemann zeta function on very short segments of
the critical line, based on the Riemann hypothesis. In particular, the
conditional solution of one problem of A.A.Karatsuba is given. Some typos of
the previous versions are corrected (in particular, the important remark of
Prof. Yan Fyodorov is taken into account). The reference to the grant of
Russian Scientific Fund is also added.Comment: 40 pages, 4 figure
Nonlocal pseudopotentials and magnetic fields
We show how to describe the coupling of electrons to non-uniform magnetic
fields in the framework of the widely used norm-conserving pseudopotential
appro ximation for electronic structure calculations. Our derivation applies to
magnetic fields that are smooth on the scale of the core region. The method is
validated by application to the calculation of the magnetic susceptibility of
molecules. Our results are compared with high quality all electron quantum
chemical results, and another recently proposed formalism.Comment: 4 pages, submitted to Physical Review Letter
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