6 problems

For a prime $p$, a Mersenne number is $M_p=2^p-1$; write $M_n$ for the Mersenne primes indexed by their prime exponents, and let $\gamma$ denote the Euler–Mascheroni constant. The…

Wright-Euler Mersenne Exponent Hypothesis. The values $C(n)$ generate candidate exponents

Malle's module-frequency conjecture. The module $H$ should arise as $Cl_2(K)$ with frequency

Let $E_1$ and $E_2$ be as in the preceding product setting, let $T\in\mathbb{Z}$ be fixed, and let $\Phi$ denote the relevant Sato–Tate trace density. Integral heuristic. The heuri…

Let $A(p)$ be the integer-valued quantity defined in the paper from the residue computation associated with the Euler number $E_{p-3}$, and let $a,b,K,L$ be the parameters occurrin…

Let $q$ be a prime power, let $p$ be an odd prime not dividing $\operatorname{char}({\mathbb F}_{q})$, and let $K$ be a quadratic extension of the rational function field…