# Tag Info

Accepted

### Freeman Dyson's approach to string theory

Dyson's A walk through Ramanujan's garden gives the background of this comment: He explains that the "seeds from Ramanujan's garden have been blowing on the wind and have been sprouting all over ...
• 180k

### Freeman Dyson's approach to string theory

I don't think it would have convinced Feynman because he didn't like the rabbit hole that string theory seemed to be going down. That instead of trying to explain some phenomenon, that they were ...
• 101
Accepted

### Is there a Cramer's conjecture for Sophie Germain primes?

Heuristics says that $n$ is Sophie Germain prime with probability roughly $1/\log^2n$. Thus the probability that $C\log^an$×consecutive numbers starting from $n$×are not Sophie Germain primes is about ...
• 104k

• 987
Accepted

### Upper bound for an infinite series of Pochhammer Symbol

The sum is $r/(1-\alpha)^{(1+r/\alpha)}$ by the binomial theorem.
• 16.5k

### How differently would we model the distribution of primes if prime gap is larger?

I think a short answer is we don't have a supply of alternative models for prime numbers lying around that make very different predictions for gaps. If a proof was found of larger prime gaps than ...
• 138k

1 vote

### On distribution of size of integer points in a subspace associated to a linear diophantine equation

This is a partial answer in one direction. Let $k=\lceil n/6\rceil$, and let $$A=6k+1, B=10k+1, C=9k+1, D=8k+1.$$ The numbers $A,B,C,D$ are pairwise coprime, larger than $n$, and all their ...
1 vote

### Generalized notion of divisor function?

There is an evident estimate: $f(n)= \frac{1}{2} \sum_{i=-b}^{i=b} \tau (n+i) + O(b)$ . P.S. That is for $f(n)=d(n,\sqrt{n})$ in your initial message.
• 357
1 vote

### Occurrence of simultaneous small remainders?

This is not always true. Suppose that $c_1+c_2=c_0$. Then $pc_1+pc_2\equiv pc_0\pmod{n}$. Hence if $pc_1\bmod n$, $pc_2\bmod n$ are in $[0, n^r]$, then $pc_0\bmod n$ is in $[0, 2n^r]$, which falls ...

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