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Results tagged with prime-number-theorem
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user 9232
The Prime Number Theorem is a theorem that describes the distribution of the primes. It says that the number of primes less than or equal to a real number $x$ is asymptotic to $\frac{x}{\ln x}$.
4
votes
Divisor sums over values of binary forms of primes
An answer regarding the use of large sieve suggested by Lucia (too long for a comment).
I guess her/his thought was along the following lines:
The divisors $d$ of $p^2+q^2$ are of order $x^2$ and …
- 3,062
7
votes
2
answers
424
views
Divisor sums over values of binary forms of primes
Let $\tau$ be the divisor function, that is
$$
\tau(n)=\sharp\{d \in \mathbb{N}, d|n\}.
$$
I was wondering if anyone has ever proved an asymptotic estimate
for the sum
$$S(x):=\sum_{p,q\leq x}\tau(p …
- 3,062