MathOverflow

consider the new form of the sieve method is as follows:$$S=\sum_{n\in I}\left(\sum_{1\le i\le k}\chi_{\mathbb P}(n+h_i)-\rho\right)\left(\sum_{\substack{d_1,\dots,d_k \\ a_1,\dots,a_k \\ d_i\mid n+h_i\forall i \\ a_i\mid d_i\forall i}}\lambda_{d_1,...

Let $K:=K(C)$ be the function field of a smooth proper curve $C$ over a finite field $k=\mathbb{F}_q$, where $q=p^r$.Let $X/K$ be an abelian variety of dimension $g$.
I can define the height of $X$ to be $$h(X):=\deg(\Omega^1_{\mathcal{X}/C}),$$where $\mathcal{X}$ is the Néron model of $X$. One of my recent research result works perfectly when $h(X)\leq \frac{p-1}{g-1}$. But I don't know does this happen often. The...

In [C Mclarty] we read
[Noether] project was to get abstract algebra away from thinking about operations on elements, such as addition or multiplication of elements in groups or rings. Her algebra would describe structures in terms of the relations between selected subsets...

On a board, a sequence of n + 1 real numbers is written, with n ≥ 1,formed by the number 1 followed by a geometric progression of n terms whose firstterm is equal to 1 and whose common ratio is equal to √2, that is, the numbers written on the board are...