## Tagged Questions

7k views

### Experimental Mathematics

I would like to ask about examples where experimentation by computers have led to major mathematical advances. Motivation I am aware about a few such cases and I think it will b …
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### 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 …
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### 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 …
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### How many surjections are there from a set of size n?

It is well-known that the number of surjections from a set of size n to a set of size m is quite a bit harder to calculate than the number of functions or the number of injections. …
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### The probability for a sequence to have small partial sums

The question Let $a_1,a_2,\dots,a_n$ be a sequence whose entries are +1 or -1. Let t be a parameter. My question is to give an estimate for the number of such sequences so that …
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### 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 |&m …
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### 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 …
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### Improving a sequence of 1s and -1s

Suppose you take a $\pm 1$ sequence and you want to "improve it" by taking pointwise limits of translates. What properties can you guarantee to get in the limit? Two examples ill …