10 problems

Let $\chi_1$ and $\chi_2$ be nontrivial, primitive Dirichlet characters modulo $q_1$ and $q_2$, respectively, with $\chi_1\chi_2(-1)=1$. Let $F_{\chi_1,\chi_2}$ be the smallest num…

Let $\chi_1$ and $\chi_2$ be nontrivial, primitive Dirichlet characters modulo $q_1$ and $q_2$, respectively, with $\chi_1\chi_2(-1)=1$. Let $S_{\chi_1,\chi_2}$ be their generalize…

Order-sensitive Dedekind-sum conjecture. There exists an absolute constant $C>0$ such that

Square-root bound conjecture. One has

Affine-linearity conjecture. Then

Let $a$ be an even integer and $b$ an odd integer, and let $s_{\sqrt{-1}}(a;b)$ and $Q(a;b)$ denote the elliptic Dedekind sum and the associated quantity used in the paper. For an…

For an integer $q\geq 2$, let $\Lambda_q$ be the set of residue classes produced by the auxiliary function $\lambda(a,t,t^{*})$, and define … The range conjecture. For every intege…

Let $S(a,b)$ be the normalized Dedekind sum, and write a value in lowest terms as $S(a,b)=k/q$, where $q\geq 2$ and $\gcd(k,q)=1$. Girstmair's necessary conditions are that…

For a fixed positive integer $b$, let $\operatorname{inv}(a,b)$ denote the inversion number and let $I_n(b)$ be its $n$th smallest value, where $1\leq n\leq6$. Six-smallest-values…

Let $b=ck$, and let $\zeta_m$ denote a primitive $m$th root of unity. The inversion polynomial $f_b(x)$ is defined by its roots indexed by the inversion numbers $\inv(a,b)$. Cyclot…