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Results tagged with analytic-number-theory
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user 169583
On the blending of real/complex analysis with number theory. The study involves distribution of prime numbers and other problems and helps giving asymptotic estimates to these.
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Formula for the sum $\sum_{n}^{\infty }\frac{\Omega (n)}{n^s}$ in terms of the Riemann zeta ...
Is there a "closed" formula for the sum $\sum_{n}^{\infty }\frac{\Omega (n)}{n^s}$ in terms of function $\zeta(s)$ (Riemann zeta ) and its derivatives? Here $\Omega (n)$ denote the total number of pri …
- 471
5
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2
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Primes in arithmetic progression $a \pmod q$
Can we prove the "Bertrand postulate" for primes $a \pmod q$, namely: there is always a prime number $p\equiv a \pmod q$ betwen $nq$ and $nq^2$ for every $n>0$ and $(a,q)=1$. (This would mean that bet …
- 471
0
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The lower bound for prime gaps
Let $p_n$ denote the $n$-th consecutive prime number and $g_n=p_{n+1}-p_n$ a prime gap. There are many results about the upper bound for $g_n$. Some of them still has astatus of conjecture, such as Fi …
- 471