A quadratic form of $p = 3k + 1$ primes
We use Zagier's one-sentence proof approach to show that a prime number $p$ admits a form $p=a^2+ab+b^2$ for some integers $a$ and $b$ if and only if $p=3$ or $p\equiv 1 \pmod{3}$.
math.NT↗
arXiv subjects
Bat-Od Battseren
Publications and source records attributed to Bat-Od Battseren.
$M_d$-multipliers of a locally compact group
We show that the space $M_d(G)$ of $M_d$-multipliers of a locally compact group $G$ is isometrically isomorphic to the Banach space of bounded functionals on the $d$-fold Haagerup tensor product of $L^1(G)$ vanishing on the kernel of the convolution map. Consequently, we see that $M_d(G)$ is isometrically isomorphic to the dual space of $X_d(G)$, the completion of $L^1(G)$ in the dual of $M_d(G)$. We also show that $M_d$-type-approximation-properties are inherited to lattices.
math.FA↗
Von Neumann equivalence and group exactness
We will show that group exactness is a von Neumann equivalence invariant. This result generalizes the previously known fact stating that group exactness is invariant under measure equivalence and W*-equivalence.
math.OA↗
Von Neumann equivalence and $M_d$ type approximation properties
We show that $M_d$-approximation-property, $M_d$-weak-amenability, and $M_d$-weak-Haagerup-property are stable under von Neumann equivalence (hence also Measure equivalence and W*-equivalence). We also show that these properties are inherited from lattices.
math.OA↗
Quasi-Hermitian pair and co-amenability
We adapt the notion of quasi-Hermition group to the pairs $(G,H)$ of discrete group $G$ and its subgroup $H$. We show that a quasi-Hermitian pair is amenable in the sense of Eymard.
math.GR↗
On the growth of Fourier multipliers
We define a sequence of functions, namely tame cuts, in the Fourier algebra $A(G)$ of a locally compact group $G$, that satisfies certain convergence and growth conditions. This new consideration allows us to give a group admitting a Fourier multiplier that is not completely bounded. Furthermore, we show that the induction map $MA(Γ)\rightarrow MA(G)$ is not always continuous. We also show how Liao's Property $(T_{Schur}, G, K)$ opposes tame cuts. Some examples are provided.
math.FA↗