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EDIT: Gerhard Paseman has given some wonderful answers to this question below. Thank you. This is an attempt to revisit this to hopefully make the question more rigorous with some notation and try to …

Let $f(x_1,\dots,x_n) \in \mathbb{Z}[x_1,\dots,x_n]$ be a polynomial for which the set of integers not represented by it is infinite. I'm curious about cases in which there exists an integer $c$ such …

For a class of concrete examples with at least asymptotically more than $n/2$ zeros on the unit circle, the Fekete polynomials, which were just mentioned recently by Franz Lemmermeyer at this question …

In Theorem 2 of their paper, "Pseudoprime values of the Fibonacci sequence, polynomials and the Euler function", Indagationes Mathematicae, Volume 17, Issue 4, pp. 611--625, Luca and Shparlinski show …

There are a number of generalizations of the Möbius function out there, which can be found by Google. But I'd just like to know if anything has been said about this: For $k \geq 2$, $k \in \mathbb{Z} …

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 …

That's a very interesting problem. If one restricts to initial point $(x,1)$, its like a generalization of the question of points $(x,y) \in (\mathbb{F}_p)^2$ so that $xy\equiv 1 \bmod p$ with $(x,y)$ …

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 …

Regarding the Galois group of the factor $g(x)=g(q,x)$of these Fekete polynomials that is conjectured to be irreducible, here is PARI code that counts, for each prime $q \equiv 1 \bmod 4$, $17 \leq q …

Also, there seem to be really interesting connections between the values of $\zeta_K(s)$ at positive integers and "higher regulators" of Bloch groups. For example, see this interesting paper: H. Gang …

Not claiming to be a real number theorist or anything of that sort...Just wondering, is one possible approach to Mark Sapir's strong conjecture (assuming an answer isn't already known) to calculate $$ …

Mr Helms, This is the $n=1$ case. Your formula gives $e_{1,q}=q$. Say we want to study how often prime $q=q_k$ divides $\prod_{p \leq x}(p-1)$. Maybe write this product as $$ \left(\prod_{i=1}^m\prod …

Now, thinking about this a bit, let's say $f$ is the function that reverses the digits, so that $f(n)$ is the number that has the digits of $n$ in base 10 reversed. I think that when estimating $$|\{n …

Hello all, I must be overlooking something, but I wonder if the systems $\Psi:\mathbb{Z}^d\rightarrow \mathbb{Z}^t$ in the Green-Tao paper "Linear Equations in Primes" could apply to this question.

Hi there, the motivation for this question is to better understand the heuristics of Mersenne primes, and I was motivated by the recent questions (Mersenne quasi-primes) and (Primes in generalized Fib …