Tagged Questions
3
votes
1answer
166 views
Proof for generalized sum of powers
Bernouli's Formula for sum of kth powers of first n natural numbers is given by:
$$f_k(n)=\frac{1}{k+1}\sum_{j=0}^k{k+1\choose j}B_j(n+1)^{k+1-j}$$
where $Bj$ is the $j^{th}$ Bernoulli Number and is ...
7
votes
0answers
147 views
Equidistribution of roots of prime cyclotomic polynomials to prime moduli
Here is a relevant - and longstanding, I'm told - conjecture. Let $f \in \mathbb{Z}[x]$ be irreducible and of degree > 1. Set
$E_p = \{x/p \: | \: 0 \leq x < p, f(x) \equiv 0 \: (p) \}$ = { ...
4
votes
1answer
143 views
Determining the Value of a Gauss Sum.
Can we evaluate the exact form of $$g\left(k,n\right)=\sum_{r=0}^{n-1}\exp\left(2\pi i\frac{r^{2}k}{n}\right) $$ for general $k$ and $n$? For $k=1$, on MathWorld we have that
...
