# Tagged Questions

**19**

votes

**2**answers

1k views

### The behavior of a certain greedy algorithm for ErdÅ‘s Discrepancy Problem

Let $N$ be a positive integer.
We want to find a completely multiplicative functions f(n) with values $\pm 1$ for $n \le N$ such that the discrepancy
$$D=\max_{n \le N} |\{\sum_{i=1}^nf(i)\}|$$
is ...

**11**

votes

**3**answers

2k views

### An elementary number theoretic infinite series

For a positive integer k, let d(k) be the number of divisors of k. So d(1)=1, d(p) =2 if p is a prime, d(6)=4, and d(12)=6.
What is the precise asymptotics of SUM_{k=1}^n 1/(kd(k))
Background:
1) ...

**73**

votes

**6**answers

8k views

### Why does the Riemann zeta function have non-trivial zeros?

This is a very basic question of course, and exposes my serious ignorance of analytic number theory, but what I am looking for is a good intuitive explanation rather than a formal proof (though a ...

**23**

votes

**5**answers

2k views

### Partial sums of multiplicative functions

It is well known that some statements about partial sums of multiplicative functions are extremely hard. For example, the Riemann hypothesis is equivalent to the assertion that ...