**8**

votes

**0**answers

152 views

### For a given even integer $k >14$ is there always a prime $p$ such that $k \leq p-3$ and $p|B_k$?

Let $k$ be a sufficiently large positive even integer. (I think $k > 14$ should do.) Can one always find a prime $p$ such that $p$ divides the numerator of the $k$-th Bernoulli number $B_k$ and $k ...

**5**

votes

**2**answers

327 views

### computing Bernoulli numbers

Is there a good way to compute the ratio ( B[n] / n! ) that occurs so often in power series coefficients? Good in the sense that you get an answer that does not overflow a double; the largest n such ...

**11**

votes

**0**answers

559 views

### A conjecture on p-divisibility of Bernoulli numbers

Is anyone aware of the history of the following conjecture on the $p$-divisibility of (the numerators) of Bernoulli numbers?
CONJECTURE: For $p$ an odd prime, and $k$ even with $2 \leq k \leq p-3$, ...

**0**

votes

**0**answers

222 views

### What is $p$-adic Fourier series?

Q1: Can we define Fourier series for a function $\mathbb{Z}_p\to \mathbb{Q}_p$?
Q2: There are (in a real case) Bernoulli polynomials which have the most simple Fourier expansion:
...

**3**

votes

**2**answers

213 views

### zeta(3) in Euler's Section 153

Jeffery Lagarias, in his recent article
Euler's constant: Euler's work and modern developments
in the AMS Bulletin, mentions that Euler obtained $\zeta(3)={{2\pi^3 b(3/2)}\over 3}$ for some "Bernoulli ...

**3**

votes

**2**answers

209 views

### Sign of coefficients

Let $a_0,a_1,\dots$ be the sequence satisfying
$$
\left(\sum_{n=0}^\infty a_n x^n\right)\left(\sum_{n=0}^\infty \frac{x^n}{n+1}\right)=1.
$$
This means that $a_0=1$ and ...

**1**

vote

**0**answers

313 views

### P-Adic poly Bernoulli numbers

we can define p-adic Bernoulli polynomials by using q-integral on $Z_p$ and T.Kim's method, But how can we define p-adic poly-Bernoulli numbers and polynomials by using integral on $Z_p$ ?

**15**

votes

**1**answer

735 views

### Riemann's $\zeta$ function and the uniform distribution on $[-1,0]$

http://math.stackexchange.com/questions/64566/riemanns-zeta-function-and-the-uniform-distribution-on-1-0
Stackexchange isn't getting really excited about this, so here it is.
The $n$th cumulant of ...