Mathematics – Number Theory
Scientist
Mathematics
Number Theory
Scientist
A few equalities involving integrals of the logarithm of the Riemann Zeta-function and equivalent to the Riemann hypothesis
A few equalities involving integrals of the logarithm of the Riemann zeta-function and equivalent to the Riemann hypothesis II
A few equalities involving integrals of the logarithm of the Riemann zeta-function and equivalent to the Riemann hypothesis III. Exponential weight functions
Both real and imaginary parts of the function F(s)=zeta(s)*Gamma(s/2)*pi**(-s/2)=xi(s)/(s*(s-1)), whose zeroes exactly coincide with the non-trivial zeroes of the Riemann zeta-function, have infinitely many zeroes for any value of Re(s)
Laser nanotraps and nanotweezers for cold atoms: 3D gradient dipole force trap in the vicinity of Scanning Near-field Optical Microscope tip
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