7 problems

For imaginary quadratic fields, let $P_M(-d)$ count primes less than $M$ that split completely and whose factors lie in the cone $C_1$. Let…

Let $L/K$ be an extension of number fields, let $M$ be the Galois closure of $L/K$, and write … If the induced representation $\operatorname{Ind}_H^G(1_H)$ contains an irreducible…

Let $\chi$ be a primitive Dirichlet character, and let $K$ be an Abelian number field. Write $\rho=\beta+i\gamma$ for nontrivial zeros of the relevant Dirichlet $L$-function…

Let the nontrivial zeros of a Dedekind zeta-function be written as $\rho=\beta+i\gamma$, and consider their positive imaginary parts $\gamma>0$. Linear independence conjecture for…

Let $L/k$ be a finite algebraic extension of number fields, and let $\zeta_L(s)$ and $\zeta_k(s)$ denote their Dedekind zeta functions. Dedekind's conjecture. The quotient … is ent…

Let $E$ range over totally real cubic number fields, and let $m_1(E)$ denote the first successive minimum of the positive definite quadratic form $Q_E$ on $\mathcal{O}_E/\mathbb Z$…

Let $\mathbb{K}$ be a quadratic extension, let $\chi$ be the associated real Dirichlet character, and let $a(k)$ be the arithmetic factor defined by the Euler product in the paper.…