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A polynomial formula for the primes (with 26 variables) was presented by Jones, J., Sato, D., Wada, H. and Wiens, D. (1976). Diophantine representation of the set of prime numbers. American Mathematic …

I came across the following problem. Find two integers, $u_{n}$ and $v_{n}$, such that $$a_{n}=4u_{n}v_{n}+(6n-1)v_{n}+(6n-1)u_{n}+8n^{2}-4n$$ divides $$b_{n}=-(2n-1)u_{n}v_{n}-(2n^{2}-3n)v_{n}-(2n …

I propose the following problem (Maybe it has a trivial solution): Let $n$ be a positive integer such that $$n\equiv1 \pmod 4.$$ Then the problem is to find a rational $x$ as a function of $n$ such …

From this page: https://en.wikipedia.org/wiki/Chebyshev_function#Asymptotics_and_bounds A theorem due to Erhard Schmidt states that, for some explicit positive constant $K$, there are infinitely ma …

Let us consider a sequence of continuous functions $g_{q}:ℝ^2\to ℝ^2$. Let $(A_{q})_{q\geq 1}$ be a sequence of compact sets in $ℝ^2$. Assuming that each function $g_{q}$ is topologically mixing in $A …

Can one let me know about the functional equation of the alternating zeta function similar to the well known for the rieman function.

I have the following question: Is there is a paper claiming that the Dirichlet series of the Hasse–Weil $L$-function (associated with an elliptic curve over rationals) is of finite order. Thank you in …

We know that the grand Riemann hypothesis is a generalisation of the Riemann hypothesis and Generalized Riemann hypothesis. My question is about the existence of a similar generalisation of the Birch …

Let us consider the following conjecture: Conjecture: There are no integer solutions of the equation $$x^{y-z}z^{x-y}=y^{x-z}$$ with $x,y,z$ distinct positive integers greater than or equal to $2$. …

The motivation for this question is the same as in my previous question in MO: https://mathoverflow.net/questions/115179/real-root-1-of-the-hasse-weil-l-function-of-c-over I am just curious to know t …

Brocard's conjecture states that: If $p_{k}$ and $p_{k+1}$ are consecutive prime numbers greater than $2$, then between $p_{k}²$ and $p_{k+1}²$ there are at least four prime numbers. I know that is st …