Friday, August 11, 2017

Heegner numbers

Heegner numbers are what I am interested in. But I plan not to go further. Because it is beyond me.
Ramanujan knew about Heegner numbers. And therefore my curiosity is a subset of his knowledge. That's the way I prefer to view my mathematical endeavours.
I have many ifs of past life. Opportunities that wasn't there. Opportunities that I just missed. But I'm confident. Just one correct friend and I can change for  better. That's the way I feel in the present.

6 comments:

Kirtivasan Ganesan said...

There are two Indians who have very high knowledge in mathematics.
One is Ramanujan and the other is Madhava of Sangamagrama.

Kirtivasan Ganesan said...

Using #PythaShastri method one can get series 1/2,1/3,1/4,1/5,1/6,1/7 and so on.
A cycle half of the above periodicity and sign varying every quarter cycle would be
1-1/3+1/5-1/7 . . .
The above is called arctangent series.
Madhava of Sangamagrama used the arctangent series and determined pi/4.
He also determined formula for errors in the above formula.
He was great.

Kirtivasan Ganesan said...

As I wrote earlier in #PythaShastri complex number post, doubling and i squared (-1) terms arises.
And Madhava of Sangamagrama has doubled and negated to obtain pi by 4 arctangent series.The movement.

Kirtivasan Ganesan said...

If you look at prime number series and observe; you will notice that Heegner numbers 7,11,19,43,67 and 163 have a lesser prime and a higher prime than them at a difference of 2,4 or 6.
For example in 5,7,11 ; 7 -5 is 2. And 11 -7 is 4.
And so is the case with others.

Kirtivasan Ganesan said...

This finishes the topic.

Kirtivasan Ganesan said...

I don't have to go further on Heegner numbers. See my post on Indo Asian hour glass.
My concepts on complex numbers, series are clear now. I possibly think like German mathematicians. Not English or French.