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Results tagged with analytic-number-theory
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user 124565
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.
23
votes
3
answers
2k
views
Why are values of Eisenstein $E_2^*$ algebraic integers?
I'm looking for a proof that the following term is an algebraic integer whenever $\tau_N=\frac{N+\sqrt{-N}}{2}$ is a quadratic irrationality with class number $1$:
$$A_N:=\sqrt{-N}\cdot\frac{E_2(\tau …
- 598
6
votes
1
answer
597
views
How to compute Coefficients in Chudnovsky's Formula?
My aim is to understand all three coefficients arising in the Chudnovsky-Formula (see also Question 300385). Two of them are easily computed, but I failed with the third:
It is known that for all $\t …
- 598
21
votes
1
answer
1k
views
Why does this quasi-modular function have integral values?
It is a well-known result that the modular function $1728J(\tau) := \frac{1728E_4(\tau)^3}{E_4(\tau)^3-E_6(\tau)^2}$ has integral values if $\tau$ has class number 1 - for example at $\tau_{163}:=\fra …
- 598