Mathematics Problem Archive

Let $f(x)\in\mathbb{C}[x]$ have $k$ monomials. Does there exist $N(k)$ such that if $$M_n:=\int_0^1f(x)^n\,dx=0\qquad(1\leq n\leq N(k)),$$ then $f=0$?...

Find a reasonable, or sharp, upper bound in terms of $m_1,m_2$ for the maximum number of simple positive-coordinate solutions of a real polynomial sys...

Is $(2m_1-1)(2m_2-1)$ the maximum number of simple solutions of a real polynomial system $f_1(x,y)=f_2(x,y)=0$, where $m_i$ is the number of monomials...

For the classical-group pairs and generic local $L$-parameters in the Gan–Gross–Prasad setting, is there exactly one relevant representation $\pi$ in ...

In the global Gan–Gross–Prasad setting, is nonvanishing of the relevant $H$-period on an irreducible cuspidal automorphic representation equivalent to...

Does there exist a nonzero polynomial on $U\otimes V\otimes W$ invariant under $SL(U)\times SL(V)\times SL(W)$ when $\dim U=\dim V=4$ and $\dim W=8$?...