Another Paper - maybe slightly OT - Euler's Totient

Hello All, I've put together another paper this time detailing some
topics in number theory and public key encryption. One topic covered
is Dirichlet convolution which is different from the convolution we
"normally" encounter in DSP and engineering. So I think you may find
this interesting.

http://www.claysturner.com/dsp/totient.pdf

As usual I appreciate any and all feedback.

Clay

p.s. I've already expanded the time reversal paper quite a bit - I
just need to wrap up the section on periodicity of the DFT. And
everybody's comments whether public or private really help me. Thanks.

On 5 Nov, 15:50, c...@claysturner.com wrote:
> Hello All, I've put together another paper this time detailing some
> topics in number theory and public key encryption. One topic covered
> is Dirichlet convolution which is different from the convolution we
> "normally" encounter in DSP and engineering. So I think you may find
> this interesting.
>
> http://www.claysturner.com/dsp/totient.pdf
>
> As usual I appreciate any and all feedback.
>
> Clay
>
> p.s. I've already expanded the time reversal paper quite a bit - I
> just need to wrap up the section on periodicity of the DFT. And
> everybody's comments whether public or private really help me. Thanks.

seems ok, mobius inversion formula would be a useful addition. In
terms of number theory, my best idea so far is the ringfield. Noting
from hw binary arithmetic is performed by hift add/sub, and noting
that 2s complement and the positions of the divisor and multiplicand,
an operation of add to self, and conditionally add multidivisor and
carry at lsbit on carry performs both multiplication and division
depending how the arrangement of data is using the right complement.

This then leads to the idea of infinitly extending the precision of
the two half words, and analytically using sin/cos to perform rotation
from division to multplication (90 degree phase difference). I have
not yet developed an effctive notation, but do believe it could have
major solution impact to certain integrals differential equations and
series summation. As differentation (sub/div) is to integration (mul/
add).

cheers
jacko

jackokring@gmail.com

paper on ringfields

http://sites.google.com/site/jackokring

bottom of page as attatchment ringfields.pdf

On Nov 7, 12:10&#4294967295;pm, jacko <jackokr...@gmail.com> wrote:
> paper on ringfields
>
> http://sites.google.com/site/jackokring
>
> bottom of page as attatchment ringfields.pdf


Very interesting paper!

For those who like the intersection of number theory and signal-
processing, the link below brings you to a paper I presented at ICASSP
about 5 years ago, linking the Riemann Zeta function to log-sampled
discrete-time systems (you may need IEEE Explore access to see
this .... sorry!)


Bob Adams



http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1415949