4 problems

Minimalist central-vanishing conjecture. If $k\equiv2\, (\mathrm{mod} {\, 4})$, then $m(f)=1$. When $k\equiv2\, (\mathrm{mod} {\, 4})$, the functional equation forces central vanis…

Let $L/\mathbb Q$ be a number-field extension and let $L_0/\mathbb Q$ be its Galois closure. Let $W(\chi)$ be the root number of the Artin $L$-function attached to $\chi$, and let…

Let $L/\mathbb Q$ be a number-field extension and let $L_0/\mathbb Q$ be its Galois closure. Let $\chi_0$ denote the trivial character, and classify irreducible characters of…

Let $\chi$ be a Dirichlet character and let $L(s,\chi)$ denote its Dirichlet $L$-function. The central-point nonvanishing conjecture. … for every Dirichlet character $\chi$. The so…