Jump to content

User:Manishkrisna108/sandbox

From Wikipedia, the free encyclopedia

welcome in the world of SANDS.

Lots of messy objets are here and there.In this page I am supposed to use letters and numbers as sand to construct models before wiki editing. somatic





Approximation by Riemann zeta zeros

[edit]

{wb:Fundamentals of Physics}

The first Riemann zeta zero wave in the sum that approximates the von Mangoldt function

The real part of the sum over the zeta zeros:

, where ρ(i) is the i-th zeta zero, peaks at primes, as can be seen in the adjoining graph, and can also be verified through numerical computation. It does not sum up to the Von Mangoldt function.[1]

The Fourier transform of the von Mangoldt function gives a spectrum with spikes at ordinates equal to imaginary part of the Riemann zeta function zeros. This is sometimes called a duality.

The Fourier transform of the von Mangoldt function gives a spectrum with imaginary parts of Riemann zeta zeros as spikes at the x-axis ordinates (right), while the von Mangoldt function can be approximated by zeta zero waves (left)

References

[edit]
  1. ^ Conrey, J. Brian (March 2003). "The Riemann hypothesis" (PDF). Notices Am. Math. Soc. 50 (3): 341–353. Zbl 1160.11341. Page 346


Erwin Schrödinger (1887 – 1961) Schrödinger shared the 1933 Nobel Prize in physics together with Paul Dirac for his contributions to quantum mechanics.

WP:COPYARTICLE, old revision of H. C. Verma which this user had just edited

See also

[edit]

Deleted image removed:

File:Anil Kumar Gain.png
Anil Kumar Gain, noted Bengali mathematician from the University of Cambridge, founder of Vidyasagar University