Yitang Zhang recently published a new attack on the Twin Primes Conjecture. Quoting Andre Granville: “The big experts in the field had already tried to make this approach w …

I define the notion of "Galois class of L functions" in the following way: $A$ is a Galois class of L functions if and only if the follwing three conditions hold simultaneously: …

Let $p$ be a prime integer, and let $(\mathbb Z/p\mathbb Z)^*$ be the set of non-zero elements of $\mathbb Z/p \mathbb Z$. Denote by $S((\mathbb Z/p \mathbb Z)^*)$ the group of per …

PART I (Initial version) Let   $P$   be the set of all primes   $2\ 3\ \ldots$.   Let $$P_d\ \ :=\ \ \{\ p\in P\ :\ \exists_{q\in P}\ \ 0 < |p-q|\le d\ \}$ …

Let $\Gamma\subseteq \Gamma'\subset SL_2(\mathbb Z)$ be congruence subgroups, and $X(\Gamma)$, $X(\Gamma')$ be the associated smooth projective modular curves over $\mathbb C$. Th …

Let $K$ be a local field with mix char, $k$ residue field. We have an exact sequence $0 \longrightarrow I \longrightarrow G_{K} \longrightarrow G_{k} \longrightarrow 0$ Then we o …

The recent sensational news on bounded gaps between primes made me wonder: what is the status of Yitang Zhang's earlier arXiv preprint on Landau-Siegel zeros? If this result is cor …

Composite numbers $n$ such that $A179382((n+1)/2)=(n-1)/(2^c)$ for some $c > 0$. I named this numbers "antiprimes". $a(1-5):92673, 143713, 3579553, 4110529, 28688897$ $a(6) > 68 …

Let $\alpha$ be any positive irrational and $\beta$ be any positive real. We have the following results. H. Weyl (1909): The fractional part of the sequence $\alpha n$ is equidist …

This question deals with the gamma factor of a primitive function of the Selberg class. Writing the functional equation of such a function $F$ as $\Phi(s)=\overline{\Phi(\overline{ …

I am usually confused by questions of the type "could such and such a problem be undecidable", because as far as I know there are two distinct possible meanings of "undecidable". …

What are the main ideas of Harald Helfgott's proof that all odd $n \geq 5$ is the sum of 3 primes?

A website ( http://www.math.unicaen.fr/~nitaj/abc.html#Consequences ) says that the $abc$ conjecture implies that there are only finitely many solutions to the equation $x^n+y^n=z^ …

The von Staudt-Clausen theorem expresses that the Bernoulli numbers' denominators have a very special form (see the wikipedia page on the theorem for more details). What interests …

I'm reading a paper On the Torsion Jacquet-Langlands correspondence by Akshay Venkatesh and Frank Calegari. Truthfully speaking I have no idea what Jacquet-Landlands is. I'm ju …