arXiv subjects

Mehmet Haluk Sengun

Publications and source records attributed to Mehmet Haluk Sengun.

23 records · Page 2Linked to original sources

arXiv2013

Arithmetic Aspects of Bianchi Groups

We discuss several arithmetic aspects of Bianchi groups, especially from a computational point of view. In particular, we consider computing the homology of Bianchi groups together with the Hecke action, connections with automorphic forms, abelian varieties, Galois representations and the torsion in the homology of Bianchi groups. Along the way, we list several open problems and conjectures, survey the related literature, presenting concrete examples and numerical data.

math.NT↗

arXiv2013

On Level One Cuspidal Bianchi Modular Forms

In this paper, we present the outcome of vast computer calculations, locating several of the very rare instances of level one cuspidal Bianchi modular forms that are not lifts of elliptic modular forms.

math.NT↗

arXiv2010

On The Torsion Homology of Non-Arithmetic Hyperbolic Tetrahedral Groups

Numerical data concerning the growth of torsion in the first homology of non-arithmetic hyperbolic tetrahedral groups are collected. The data provide support the speculations of Bergeron and Venkatesh on the growth of torsion homology and the regulators for lattices in SL(2,C).

math.NT↗

arXiv2010

On the Integral Cohomology of Bianchi groups

Extensive and systematic machine computations are carried out to investigate the integral cohomology of the Euclidean Bianchi groups and their congruence subgroups. The collected data give insight on several aspects, including the asymptotic behaviour of the torsion in the first homology. Along with the experimental work, some basic properties of the integral cohomology are recorded with an eye towards the liftibility issue of Hecke eigenvalue systems.

math.NT↗

arXiv2008

Weight Reduction for Mod l Bianchi Modular Forms

Let K be an imaginary quadratic field with class number one and ring of integers O. We prove that mod l, a system of Hecke eigenvalues occurring in the first cohomology group of some congruence subgroup Gamma of SL(2,O) can be realized in the first cohomology with trivial coefficients after increasing the level of Gamma by l.

math.NT↗