8 problems

Continuous multiple Dedekind zeta conjecture. For fixed large $M$, as $T$ varies, the distribution of the number of represented primes is given by

Imaginary quadratic pair-prime conjecture. The distribution is

Let $r\geq 1$, and let an inter-trivial zero (ITZ) of $\zeta_r(s)$ mean a real zero on the negative real line other than the known zeros at the negative even integers. For any…

Let $r\geq 2$. For $2\leq k\leq r$, let $I_r(k)$ denote the number of inter-admissible zeros of $\zeta_r(s)$ in the interval $(1/k,1/(k-1))$, where an inter-admissible zero is a re…

Let $r\geq 1$ and $n\in\mathbb{N}$. An inter-trivial zero (ITZ) is a real zero of $\zeta_r(s)$ lying between consecutive trivial zeros on the negative real axis. Inter-trivial zero…

Let $r\geq 2$. For $2\leq k\leq r$, let $I_r(k)$ denote the number of inter-argument zeros (IAZs) of $\zeta_r(s)$ in the interval $(1/k,1/(k-1))$. Simple IAZ conjecture. All IAZs o…

Critical-line analogue conjecture. The line

Ikeda–Matsuoka–Nagata's conjecture. The boundary of this region is the double analogue of the critical line of the Riemann zeta function. This conjecture arises from mean-value res…