Cohomology of Congruence Subgroups of SU (2, 1) p and Hodge Cycles on Some Special Complex Hyperbolic Surfaces

2000 ◽  
pp. 1-15 ◽  
Author(s):  
Don Blasius ◽  
Jonathan Rogawski
Keyword(s):  
Hyperbolic Surfaces ◽  
Congruence Subgroups ◽  
Special Complex

Geometric Schottky groups and non-compact hyperbolic surfaces with infinite genus

2021 ◽  
Vol 76 ◽  
pp. 101752
Author(s):  
John A. Arredondo ◽  
Camilo Ramírez Maluendas
Keyword(s):  
Schottky Groups ◽  
Hyperbolic Surfaces

scholarly journals Twisted 6d (2, 0) SCFTs on a circle

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Zhihao Duan ◽  
Kimyeong Lee ◽  
June Nahmgoong ◽  
Xin Wang
Keyword(s):  
Lie Groups ◽  
Point Of View ◽  
Partition Functions ◽  
Congruence Subgroups ◽  
Gauge Groups ◽  
Simple Lie Groups ◽  
Instanton Contribution ◽  
Elliptic Genera ◽  
Supersymmetric Gauge ◽  
The One

Abstract We study twisted circle compactification of 6d (2, 0) SCFTs to 5d $$ \mathcal{N} $$ N = 2 supersymmetric gauge theories with non-simply-laced gauge groups. We provide two complementary approaches towards the BPS partition functions, reflecting the 5d and 6d point of view respectively. The first is based on the blowup equations for the instanton partition function, from which in particular we determine explicitly the one-instanton contribution for all simple Lie groups. The second is based on the modular bootstrap program, and we propose a novel modular ansatz for the twisted elliptic genera that transform under the congruence subgroups Γ0(N) of SL(2, ℤ). We conjecture a vanishing bound for the refined Gopakumar-Vafa invariants of the genus one fibered Calabi-Yau threefolds, upon which one can determine the twisted elliptic genera recursively. We use our results to obtain the 6d Cardy formulas and find universal behaviour for all simple Lie groups. In addition, the Cardy formulas remain invariant under the twist once the normalization of the compact circle is taken into account.

scholarly journals On some automorphic properties of Galois traces of class invariants from generalized Weber functions of level 5

2019 ◽  
Vol 17 (1) ◽  
pp. 1631-1651
Author(s):  
Ick Sun Eum ◽  
Ho Yun Jung
Keyword(s):  
Modular Forms ◽  
Fourier Coefficients ◽  
Singular Values ◽  
Congruence Subgroups ◽  
Maass Form ◽  
Weakly Holomorphic Modular Forms ◽  
Reciprocity Law ◽  
Class Invariants ◽  
Higher Genus ◽  
Holomorphic Modular Forms

Abstract After the significant work of Zagier on the traces of singular moduli, Jeon, Kang and Kim showed that the Galois traces of real-valued class invariants given in terms of the singular values of the classical Weber functions can be identified with the Fourier coefficients of weakly holomorphic modular forms of weight 3/2 on the congruence subgroups of higher genus by using the Bruinier-Funke modular traces. Extending their work, we construct real-valued class invariants by using the singular values of the generalized Weber functions of level 5 and prove that their Galois traces are Fourier coefficients of a harmonic weak Maass form of weight 3/2 by using Shimura’s reciprocity law.

Vampix, a multimicroprocessor control system adaptable to special complex machines

1987 ◽  
Vol 21 (1-5) ◽  
pp. 325-330 ◽  
Author(s):  
Dipl Ing. Drazen FLEGO ◽  
Herbert Schweinzer
Keyword(s):  
Control System ◽  
Special Complex

Asymptotic Estimates of the First Eigenvalue of the p-Laplacian

2003 ◽  
Vol 3 (2) ◽  
Author(s):  
Bruno Colbois ◽  
Ana-Maria Matei
Keyword(s):  
Direct Application ◽  
Parameter Family ◽  
Precise Estimate ◽  
First Eigenvalue ◽  
Asymptotic Estimates ◽  
Hyperbolic Surfaces ◽  
The First Eigenvalue

AbstractWe consider a 1-parameter family of hyperbolic surfaces M(t) of genus ν which degenerate as t → 0 and we obtain a precise estimate of λAs a direct application, we obtain that the quotientTo prove our results we use in an essential way the geometry of hyperbolic surfaces which is very well known. We show that an eigenfunction for λ

Subgroup growth and congruence subgroups

1995 ◽  
Vol 119 (1) ◽  
pp. 267-295 ◽  
Author(s):  
Alexander Lubotzky
Keyword(s):  
Congruence Subgroups ◽  
Subgroup Growth

scholarly journals Isometry groups of infinite-genus hyperbolic surfaces

2021 ◽  
Author(s):  
Tarik Aougab ◽  
Priyam Patel ◽  
Nicholas G. Vlamis
Keyword(s):  
Hyperbolic Surfaces ◽  
Isometry Groups

scholarly journals Monitoring the dynamic behaviors of the Bosporus Bridge by GPS during Eurasia Marathon

2007 ◽  
Vol 14 (4) ◽  
pp. 513-523 ◽  
Author(s):  
H. Erdoğan ◽  
B. Akpınar ◽  
E. Gülal ◽  
E. Ata
Keyword(s):  
Frequency Domain ◽  
Element Model ◽  
Traffic Load ◽  
Suspension Bridges ◽  
Engineering Structures ◽  
Low Frequencies ◽  
Temperature Changes ◽  
Bridge Responses ◽  
Special Complex ◽  
Short Time

Abstract. Engineering structures, like bridges, dams and towers are designed by considering temperature changes, earthquakes, wind, traffic and pedestrian loads. However, generally, it can not be estimated that these structures may be affected by special, complex and different loads. So it could not be known whether these loads are dangerous for the structure and what the response of the structures would be to these loads. Such a situation occurred on the Bosporus Bridge, which is one of the suspension bridges connecting the Asia and Europe continents, during the Eurasia Marathon on 2 October 2005, in which 75 000 pedestrians participated. Responses of the bridge to loads such as rhythmic running, pedestrian walking, vehicle passing during the marathon were observed by a real-time kinematic (RTK) Global Positioning System (GPS), with a 2.2-centimeter vertical accuracy. Observed responses were discussed in both time domain and frequency domain by using a time series analysis. High (0.1–1 Hz) and low frequencies (0.00036–0.01172 Hz) of observed bridge responses under 12 different loads which occur in different quantities, different types and different time intervals were calculated in the frequency domain. It was seen that the calculated high frequencies are similar, except for the frequencies of rhythmic running, which causes a continuously increasing vibration. Any negative response was not determined, because this rhythmic effect continued only for a short time. Also when the traffic load was effective, explicit changes in the bridge movements were determined. Finally, it was seen that bridge frequencies which were calculated from the observations and the finite element model were harmonious. But the 9th natural frequency value of the bridge under all loads, except rhythmic running could not be determined with observations.

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