Yevgeny Zaytman

activity

20172022

most citedOn the bounded generation of arithmetic

SL_{2}

7 citations · 10 across the 7 of their papers we have counts for

collaborators

9 papers

math.NT2022

Isogeny complexes of superspecial abelian varieties

Bruce W. Jordan, Yevgeny Zaytman

We consider the structures formed by isogenies of abelian varieties with polarizations that are not necessarily principal, specifically with the $[ℓ]$ -polarizations we have prev…

math.NT2020

Isogeny graphs of superspecial abelian varieties and Brandt matrices

Bruce W. Jordan, Yevgeny Zaytman

Fix primes $p$ and $ℓ$ with $ℓ \neq = p$ . If $(A, λ)$ is a $g$ -dimensional principally polarized abelian variety, an $(ℓ)^{g}$ -isogeny of $(A, λ)$ has kernel a maximal isotropic…

math.NT2020

Quotient graphs and amalgam presentations for unitary groups over cyclotomic rings

Colin Ingalls, Bruce W. Jordan, Allan Keeton +2

Suppose $4∣ n$ , $n \geq 8$ , $F = F_{n} = Q (ζ_{n} + ζ ˉ_{n})$ , and there is one prime $p = p_{n}$ above $2$ in $F_{n}$ . We study amalgam presentations for $\operatornam…

math.NT2019

Sarnak's conjecture in quantum computing, cyclotomic unitary group coranks, and Shimura curves

Colin Ingalls, Bruce W. Jordan, Allan Keeton +2

Sarnak's conjecture in quantum computing concerns when the groups $PU_{2}$ and $PSU_{2}$ over cyclotomic rings $Z [ζ_{n}, 1/2]$ with $ζ_{n} = e^{2 π i / n}$ …

math.NT2019

The Zariski closure of integral points on varieties parametrizing periodic continued fractions

Bruce W. Jordan, Adam Logan, Yevgeny Zaytman

Let $R$ be the ring of $S$ -integers in a number field $K$ . Let $B = {β, β^{*}}$ be the multi-set of roots of a nonzero quadratic polynomial over $R$ . There are varieti…

math.NT2019

The Clifford-cyclotomic group and Euler-Poincaré characteristics

Colin J. Ingalls, Bruce W. Jordan, Allan Keeton +2

For an integer $n \geq 8$ divisible by $4$ , let $R_{n} = Z [ζ_{n}, 1/2]$ and let $U_{2} (R_{n})$ be the group of $2 \times 2$ unitary matrices with entries in $R_{n}$ . Set $…

math.NT2019

Integral points on varieties defined by matrix factorization into elementary matrices

Bruce W. Jordan, Yevgeny Zaytman

Let $O$ be the ring of $S$ -integers in a number field $K$ . For $A \in SL_{2} (O)$ and $k \geq 1$ , we define matrix-factorization varieties $V_{k} (A)$ over ${\ma…

math.NT2018★ 7 cited

On the bounded generation of arithmetic $SL_{2}$

Bruce W. Jordan, Yevgeny Zaytman

Let $K$ be a number field and $O$ be the ring of $S$ -integers in $K$ . Morgan, Rapinchuck, and Sury have proved that if the group of units $O^{\times}$ is infi…

math.NT2017★ 3 cited

Statistics of $K$ -groups modulo $p$ for the ring of integers of a varying quadratic number field

Bruce W. Jordan, Zev Klagsbrun, Bjorn Poonen +2

For each odd prime $p$ , we conjecture the distribution of the $p$ -torsion subgroup of $K_{2 n} (O_{F})$ as $F$ ranges over real quadratic fields, or over imaginary quadratic…

Isogeny complexes of superspecial abelian varieties

Isogeny graphs of superspecial abelian varieties and Brandt matrices

Quotient graphs and amalgam presentations for unitary groups over cyclotomic rings

Sarnak's conjecture in quantum computing, cyclotomic unitary group coranks, and Shimura curves

The Zariski closure of integral points on varieties parametrizing periodic continued fractions

The Clifford-cyclotomic group and Euler-Poincaré characteristics

Integral points on varieties defined by matrix factorization into elementary matrices

On the bounded generation of arithmetic SL2​

Statistics of K-groups modulo p for the ring of integers of a varying quadratic number field

On the bounded generation of arithmetic $SL_{2}$

Statistics of $K$ -groups modulo $p$ for the ring of integers of a varying quadratic number field