4,464 reputation
816
bio website motls.blogspot.com
location Czech Republic
age 40
visits member for 2 years, 11 months
seen Mar 12 at 7:48

Hi, I am a string theorist and a publicist.


Mar
6
comment Why does $1+2+3+\dots = {-1\over 12}$?
Sure, it's a completely analogous sum. Just like $1+2+3+\dots$ quantifies the ground state energy in 1+1 dimensions (of a string), $1+1+1+\dots$ quantifies the ground state's charge (of a system of free fermions, for example). It's really the reason why the two degenerate states $|0\rangle$ and $c_0|0\rangle$ have ghost numbers $\pm 1/2$, for example.
Feb
10
comment Why does $1+2+3+\dots = {-1\over 12}$?
It might be but it is a wrong conclusion. The key property of this $\infty$, which may be subtracted by a counterterm, is that it is independent of all independent variables, so it is formally a scale-invariant constant, and $0$ is the number to be associated with it. The fact that the sum of integers equals $-1/12$ is perhaps the most important fact about mathematics among the laymen - and among mathematicians without breadth and depth.
Feb
8
answered Equivalence of Two Lorentz Groups
Jan
24
comment $1 + 1 + 1 +\cdots = -\frac{1}{2}$
Dear @Pedro, I am saying that $\zeta(2k+1)$ are transcendental numbers because I am ready to bet all my wealth on the validity of the claim. After all, even $\pi^n$ are transcendental numbers for rational nonzero values of $n$ so even zeta of even positive integers are (provably) transcendental. But the zetas of odd positive integers are (I claim without a rigorous proof) much more transcendental than the powers of $\pi$. I never claimed that I had a rigorous proof of the transcendentality but if you want to claim that I said something incorrect, you should have a proof which you don't have.
Jan
24
comment $1 + 1 + 1 +\cdots = -\frac{1}{2}$
Nope, it's just believed by me and almost everyone that they're transcendental. The much "easier" proof that zeta(3) is irrational came just recently, in 1978, see en.wikipedia.org/wiki/Ap%C3%A9ry's_theorem
Jan
23
comment $1 + 1 + 1 +\cdots = -\frac{1}{2}$
Nice, +1. An alternative calculation of $\zeta(0)=-1/2$ appears early in this article: motls.blogspot.com/2014/01/… - See my comment under the OP's question for 4 more articles about the topic if you wish...
Jan
23
comment $1 + 1 + 1 +\cdots = -\frac{1}{2}$
Five more articles with 8 different ways to compute the sum of integers (most of the methods extend to the "sum of ones", too) etc.: motls.blogspot.com/2007/09/… motls.blogspot.com/2011/07/… motls.blogspot.com/2014/01/… motls.blogspot.com/2014/01/… motls.blogspot.com/2014/01/…
Jan
11
comment Why does $1+2+3+\dots = {-1\over 12}$?
"Incorrect", "not right", and "opposite of right" are the same thing, also known as "synonyma".
Sep
20
comment Showing Dirac Delta Behavior
Well, I think you would also have to discuss that the negative regions of $(\sin x)/x$ don't combine to other distributions like $\delta'$ etc. But otherwise OK, I upvote it.
Jun
25
comment Fourier transform of a signal sequence?
I would be sort of surprised if there is an analytic formula for the Fourier transform of this contrived function.
Jun
18
awarded  Good Answer
May
29
revised How find the number of $z$,such that$ |a^2-b^2-b+1|\le 10$
added 365 characters in body
May
29
answered How find the number of $z$,such that$ |a^2-b^2-b+1|\le 10$
May
28
answered Evaluate integral in terms of Gamma function
May
24
revised Grover Algorithm Orthogonal vectors
added 15 characters in body
May
24
comment Grover Algorithm Orthogonal vectors
Sorry, I made a mistake. I meant that $\omega$ and $s'$ are orthogonal. My answer is hopefully fixed. I don't understand the question "how I will be able to define $\sqrt{N}|\omega\rangle$". It's just multiplication, right? One should know how to multiply vectors by numbers.
May
24
answered Grover Algorithm Orthogonal vectors
May
7
awarded  Yearling
Feb
3
awarded  Enlightened
Feb
3
awarded  Nice Answer