We discuss the relationship between Penner's λ-lengths, with both Fermat's theorem on representation of a prime as the sum of squares and the Markoff spectrum. The text follows pretty closely the two talks I gave in June 2021 for the online meeting. We have included an informal discussion of some work on sums of squares which was suggested by questions raised at the meeting
We give a new proof of Moeckel’s result that for any finite index subgroup of the modular group, alm...
The volume $\mathscr{B}_{\Sigma}^{{\rm comb}}(\mathbb{G})$ of the unit ball -- with respect to the c...
The four square theorem was proved by Lagrange in 1770; every positive integer is the sum of four sq...
This article concerns the arithmetics of binary quadratic forms with integer coefficients, the De Si...
Let C be the boundary surface of a strictly convex d-dimensional body. Andrews obtained an upper bou...
ABSTRACT. We survey some of our recent results on length series identities for hyperbolic (cone) sur...
In these notes we give as ummary of the main developments in the Prime Geodesic Theorem on hyperboli...
Among all bi-Perron numbers, we characterise those all of whose Galois conjugates are real or unimod...
The purpose of this thesis is to discuss Markoff Numbers, their associated binary quadratic forms, t...
For Γ a cofinite Kleinian group acting on H3, we study the prime geodesic theorem on M = Γ\H3, which...
Abstract. Taking the integrated Chebyshev-type counting function of the appropriate order, we improv...
In 1992, Reid asked whether hyperbolic 3-manifolds with the same geodesic length spectra are necessa...
In this thesis we will prove the following new identity Σγ 1/(1 + exp |γ|) = 1/2, where the su...
Erlandsson and Zakeri gave a very precise description of the Margulis region associated to cusps of ...
The theory of numbers continues to occupy a central place in modern mathematics because of both its ...
We give a new proof of Moeckel’s result that for any finite index subgroup of the modular group, alm...
The volume $\mathscr{B}_{\Sigma}^{{\rm comb}}(\mathbb{G})$ of the unit ball -- with respect to the c...
The four square theorem was proved by Lagrange in 1770; every positive integer is the sum of four sq...
This article concerns the arithmetics of binary quadratic forms with integer coefficients, the De Si...
Let C be the boundary surface of a strictly convex d-dimensional body. Andrews obtained an upper bou...
ABSTRACT. We survey some of our recent results on length series identities for hyperbolic (cone) sur...
In these notes we give as ummary of the main developments in the Prime Geodesic Theorem on hyperboli...
Among all bi-Perron numbers, we characterise those all of whose Galois conjugates are real or unimod...
The purpose of this thesis is to discuss Markoff Numbers, their associated binary quadratic forms, t...
For Γ a cofinite Kleinian group acting on H3, we study the prime geodesic theorem on M = Γ\H3, which...
Abstract. Taking the integrated Chebyshev-type counting function of the appropriate order, we improv...
In 1992, Reid asked whether hyperbolic 3-manifolds with the same geodesic length spectra are necessa...
In this thesis we will prove the following new identity Σγ 1/(1 + exp |γ|) = 1/2, where the su...
Erlandsson and Zakeri gave a very precise description of the Margulis region associated to cusps of ...
The theory of numbers continues to occupy a central place in modern mathematics because of both its ...
We give a new proof of Moeckel’s result that for any finite index subgroup of the modular group, alm...
The volume $\mathscr{B}_{\Sigma}^{{\rm comb}}(\mathbb{G})$ of the unit ball -- with respect to the c...
The four square theorem was proved by Lagrange in 1770; every positive integer is the sum of four sq...
.png%3Fwidth%3D300&w=3840&q=75)
Add to ORKG