Browsing by Subject "Modular group"

Now showing 1 - 3 of 3

Open Access
Alexander modules of trigonal curves
(2021-01) Üçer, Melih
We classify the monodromy Alexander modules of non-isotrivial trigonal curves.
Open Access
Construction of modular forms with Poincaré series
(2010) Güneş, Çisem
In this thesis, we construct holomorphic modular forms of integral weight k > 2 for the principle congruence subgroup Γ( ¯ N) by means of Poincar´e series. We start by providing the necessary background information on modular forms. Then, we show that Poincar´e series are in fact holomorphic modular forms and we obtain explicit formulas for their Fourier coefficients. For the special case when Poincar´e series are Eisenstein series, their Fourier coefficients become relatively simple. We give Fourier coefficients of the Eisenstein series belonging to the principle congruence subgroup. Finally, as an application of what has been studied, we construct Eisenstein series for the Hecke congruence supgroup.
Open Access
On the Alexander invariants of trigonal curves
(Springer - Verlag Italia Srl, 2021-01-02) Üçer, Melih
We show that most of the genus-zero subgroups of the braid group B3 (which are roughly the braid monodromy groups of the trigonal curves on the Hirzebruch surfaces) are irrelevant as far as the Alexander invariant is concerned: there is a very restricted class of “primitive” genus-zero subgroups such that these subgroups and their genus-zero intersections determine all the Alexander invariants. Then, we classify the primitive subgroups in a special subclass. This result implies the known classification of the dihedral covers of irreducible trigonal curves.