scholarly journals Integrable systems and modular forms of level 2

2006 ◽  
Vol 39 (50) ◽  
pp. 15341-15353 ◽  
Author(s):  
Mark J Ablowitz ◽  
Sarbarish Chakravarty ◽  
Heekyoung Hahn
2021 ◽  
Vol 9 ◽  
Author(s):  
Younghan Bae ◽  
Tim-Henrik Buelles

Abstract We prove a conjecture of Maulik, Pandharipande and Thomas expressing the Gromov–Witten invariants of K3 surfaces for divisibility 2 curve classes in all genera in terms of weakly holomorphic quasi-modular forms of level 2. Then we establish the holomorphic anomaly equation in divisibility 2 in all genera. Our approach involves a refined boundary induction, relying on the top tautological group of the moduli space of smooth curves, together with a degeneration formula for the reduced virtual fundamental class with imprimitive curve classes. We use double ramification relations with target variety as a new tool to prove the initial condition. The relationship between the holomorphic anomaly equation for higher divisibility and the conjectural multiple cover formula of Oberdieck and Pandharipande is discussed in detail and illustrated with several examples.


2015 ◽  
Vol 26 (05) ◽  
pp. 1550034 ◽  
Author(s):  
Fabien Cléry ◽  
Gerard van der Geer ◽  
Samuel Grushevsky

We study vector-valued Siegel modular forms of genus 2 on the three level 2 groups Γ[2] ◁ Γ1[2] ◁ Γ0[2] ⊂ Sp(4, ℤ). We give generating functions for the dimension of spaces of vector-valued modular forms, construct various vector-valued modular forms by using theta functions and describe the structure of certain modules of vector-valued modular forms over rings of scalar-valued Siegel modular forms.


Author(s):  
Douglas William Jones

Within the past 20 years, archaeobotanical research in the Eastern United States has documented an early agricultural complex before the dominance of the Mesoamerican domesticates (corn, beans, and squash) in late prehistoric and historic agricultural systems. This early agricultural complex consisted of domesticated plants such as Iva annua var.macrocarpa (Sumpweed or Marshelder), Hellanthus annuus (Sunflower) and Chenopodium berlandieri, (Goosefoot or Lasbsquarters), and heavily utilized plants such as Polygonum erectum (Erect Knotweed), Phalaris caroliniana (May grass), and Hordeum pusillum (Little Barley).Recent research involving the use of Scanning Electron Microscopy (SEM) specifically on Chenopodium has established diagnostic traits of wild and domesticated species seeds. This is important because carbonized or uncarbonized seeds are the most commonly recovered Chenopodium material from archaeological sites. The diagnostic seed traits assist archaeobotanists in identification of Chenopodium remains and provide a basis for evaluation of Chenopodium utilization in a culture's subsistence patterns. With the aid of SEM, an analysis of Chenopodium remains from three Late Prehistoric sites in Northwest Iowa (Blood Run [Oneota culture], Brewster [Mill Creek culture], and Chan-Ya-Ta [Mill Creek culture]) has been conducted to: 1) attempt seed identification to a species level, 2) evaluate the traits of the seeds for classification as either wild or domesticated, and 3) evaluate the role of Chenopodium utilization in both the Oneota and Mill Creek cultures.


2018 ◽  
Author(s):  
Handan Özek Erkuran ◽  
Şermin Yalin Sapmaz ◽  
Ahmet Herdem ◽  
Masum Öztürk ◽  
Öznur Bilaç ◽  
...  

1998 ◽  
Vol 10 (1-3) ◽  
pp. 57-72 ◽  
Author(s):  
K. S. B. Keats-Rohan

The COEL database and database software, a combined reference and research tool created by historians for historians, is presented here through Screenshots illustrating the underlying theoretical model and the specific situation to which that has been applied. The key emphases are upon data integrity, and the historian's role in interpreting and manipulating what is often contentious data. From a corpus of sources (Level 1) certain core data are extracted for separate treatment at an interpretive level (Level 3), based upon a master list of the core data (Level 2). The core data are interdependent: each record in Level 2 is of interest in itself; and it either could or should be associated with an(other) record(s) as a specific entity. Sometimes the sources are ambiguous and the association is contentious, necessitating a probabilty-coding approach. The entities created by the association process can then be treated at a commentary level, introducing material external to the database, whether primary or secondary sources. A full discussion of the difficulties is provided within a synthesis of available information on the core data. Direct access to the source texts is only ever a mouse click away. Fully query able, COEL is formidable look-up and research tool for users of all levels, who remain free to exercise an alternative judgement on the associations of the core data. In principle, there is no limit on the type of text or core data that could be handled in such a system.


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