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Results tagged with analytic-number-theory
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user 130745
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.
-1
votes
1
answer
239
views
Enquiry on an equality involving the Riemann zeta function
Let $\zeta$ denote the Riemann zeta function. Does there exist a $t\geq 0$ such that
$$\Re(1/4 + t^2)\zeta(1/2 + it)=2t\arg \zeta(1/2 + it) + 2(1/4 + t^2)\ ?$$
- 105k
3
votes
1
answer
309
views
Closed form for an integral involving the Riemann zeta function at the critical line
After seeing this question $L_2$ bounds for $\zeta(1/2 + it)$ and a related integral i became curious if/how the approach in the answer by reuns can be applied to evaluate
$$I_{a,b}=\int_{-\infty}^{ …
- 23k