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Results tagged with analytic-number-theory
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user 18494
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.
11
votes
Every prime number > 19 divides one plus the product of two smaller primes?
Perhaps this might be another perspective on this problem. In an answer to a question I had previously asked on Math Overflow, "A generalized Möbius function?", the following paper of Addison was cite …
- 1,075
5
votes
Using Vinogradov's theorem for finding prime solutions to a linear equation (an exercise fro...
Hello,
I too would be very curious about this bound and will think further about this. The nice thing about the $u_i(y)$, as I recall my advisor having told me, is that the estimates for geometric su …
9
votes
1
answer
524
views
Infimums of exponential sums involving primes
Hi, I don't know if this question is appropriate for Math Overflow but I was wondering if there is anything known about the following: Let
$$
S(\alpha) = \sum_{n \leq x}\Lambda(n)e(n\alpha).
$$
Then …
- 1,075
5
votes
2
answers
652
views
How are these number-theoretical constants actually distributed?
I'm very curious about this and would be really grateful for any help or comments in this direction. If we consider any of the following number-theoretical constants:
1)The various singular series a …
- 1,075
4
votes
Mertens-like sum in arithmetic progressions
This paper I believe might give such estimates:
Languasco, A.; Zaccagnini, A. A note on Mertens' formula for arithmetic progressions. J. Number Theory 127 (2007), no. 1, 37–46
Theorem 2 there works …
- 1,075
3
votes
Primes and Ackermann's function
Hartley (http://primes.utm.edu/curios/page.php/71.html) gives that 13 and 71 divide $A(m,n)$ for sufficiently large $m$.
Since $\{A(m+1,n): n \geq N\} \subset \{A(m,n): n\geq A(m+1,N-1)\}$, we need o …
- 1,075
4
votes
1
answer
920
views
Primes and Ackermann's function
If $A(m,n)$ is Ackermann's function, and $c$ is a fixed integer, are there any heuristics/conjectures/obvious things that can be said about primes of the form $A(m,n)+c$, $m \geq 4$,at all?
EDIT:
I …
- 1,075