## 15 Citations

Modular forms on Hecke’s modular groups

- Mathematics
- 1973

Let H={-r=x+iy:y>0}. Let A>0, k>O, y=I1. Let M(Q, k, y) denote the set of functions f for which f(r)= .D=o ane2'i"rli and f(-1/T)=y(&/i)kf(T), for all T r H. Let MO(A, k, y) denote the set of feM(A,…

A Hecke Correspondence for Automorphic Integrals with Infinitely Many Poles

- Mathematics
- 2017

A Hecke Correspondence for Automorphic Integrals With Infinitely Many Poles Haider Ebrahim Yesuf Addis Ababa University, 2017 In 1936 Hecke proved a correspondence theorem between Dirichlet series…

CONVEX STANDARD FUNDAMENTAL DOMAIN FOR SUBGROUPS OF HECKE GROUPS

- Mathematics
- 2011

It is well known that if a convex hyperbolic polygon is constructed as a fundamental domain for a subgroup of SL(2,ℝ), then its translates by the group form a locally finite tessellation and its…

Discrete free products of two complex cyclic matrix groups

- Mathematics
- 1979

Observe that the elements of ftxUf^ have infinite order, while those of ft2Uft3 have finite order. We will prove that whenever A e ft and B e ft do not both have a fixed point on L, then the group…

Continued Fractions and Hyperbolic Geometry

- Mathematics
- 2015

This thesis uses hyperbolic geom etry to study various classes of both real and com plex continued fractions. This intuitive approach gives insight into the theory of continued fractions that is not…

Log-Polynomial Period Functions for Hecke Groups

- Mathematics
- 1999

In this article we shall determine the automorphic integrals of positive and negative integral weight associated with the full modular group and some Hecke groups. This will be done by using the…

On universally optimal lattice phase transitions and energy minimizers of completely monotone potentials

- Mathematics
- 2021

. We consider the minimizing problem for energy functionals with two types of competing particles and completely monotone potential on a lattice. We prove that the minima of sum of two completely…

On the regular part of the Bloch Green’s function for the Laplacian: analytical formula and critical points

- Mathematics
- 2021

This paper is concerned with the regular part of the Bloch Green’s function in a Wigner–Seitz lattice cell. We first give a new fast converging series expression. Then we derive explicit expression…

Log-polynomial period functions for nondiscrete Hecke groups

- Mathematics
- 1999

Existence of automorphic integrals associated with nondiscrete Hecke groups will be considered. Multiplier systems for some of these groups will be discussed.

Nonhexagonal Lattices From a Two Species Interacting System

- Materials ScienceSIAM J. Math. Anal.
- 2020

A two species interacting system motivated by the density functional theory for triblock copolymers contains long range interaction that affects the two species differently. In a two species periodic…

## References

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Mathematische Werke

- HistoryNature
- 1948

VERSATILITY is the most delusive of the fairy gifts ; the men of genius on whom it was bestowed otherwise than in subtle malevolence can be counted on the fingers. In the age of Euler himself, Johann…

Dirichlet Series, Modular Functions, and Quadratic Forms

- Dirichlet Series, Modular Functions, and Quadratic Forms
- 1938