Daniel E. Martin

most citedConnectivity of Markoff mod-p graphs and maximal divisors

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math.NT2025

Markoff triples and Nielsen equivalence in $SL_{2} (F_{p})$

Daniel E. Martin

In 2013, Darryl McCullough and Marcus Wanderley made a series of conjectures that describe the Nielsen equivalence classes and $T_{2}$ -equivalence classes of pairs of generators for…

math.NT2025

A new proof of Chen's theorem for Markoff graphs

Daniel E. Martin

In 2021, Chen proved a congruence for the degree of a certain map on the space of covers of elliptic curves. He concluded as a corollary that the size of any connected component of…

math.NT2025

Lower bounds on the $ℓ$ -rank of ideal class groups

Daniel E. Martin

For a prime number $ℓ$ and an extension of number fields $K / F$ , we prove new lower bounds on the $ℓ$ -rank of the ideal class group of $K$ based on prime ramification in $K / F$ …

math.NT2023★ 1 cited

Connectivity of Markoff mod-p graphs and maximal divisors

Jillian Eddy, Elena Fuchs, Matthew Litman +2

Markoff mod- $p$ graphs are conjectured to be connected for all primes $p$ . In this paper, we use results of Chen and Bourgain, Gamburd, and Sarnak to confirm the conjecture for all…

Markoff triples and Nielsen equivalence in SL2​(Fp​)

A new proof of Chen's theorem for Markoff graphs

Lower bounds on the ℓ-rank of ideal class groups

Connectivity of Markoff mod-p graphs and maximal divisors

Markoff triples and Nielsen equivalence in $SL_{2} (F_{p})$

Lower bounds on the $ℓ$ -rank of ideal class groups