Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
String-Theory Realization of Modular Forms for Elliptic Curves with Complex Multiplication
Download
index.pdf
Date
2019-04-01
Author
Kondo, Satoshi
Watari, Taizan
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
425
views
149
downloads
Cite This
It is known that the L-function of an elliptic curve defined over Q is given by the Mellin transform of a modular form of weight 2. Does that modular form have anything to do with string theory? In this article, we address a question along this line for elliptic curves that have complex multiplication defined over number fields. So long as we use diagonal rational N=(2,2) superconformal field theories for the string-theory realizations of the elliptic curves, the weight-2 modular form turns out to be the Boltzmann-weighted (qL0-c/24-weighted) sum of U(1) charges with FeiF insertion computed in the Ramond sector.
Subject Keywords
Mathematical Physics
,
Statistical and Nonlinear Physics
URI
https://hdl.handle.net/11511/66167
Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
DOI
https://doi.org/10.1007/s00220-019-03302-0
Collections
Natural Sciences and Mathematics, Article
Suggestions
OpenMETU
Core
SYMMETRIC SPACE PROPERTY AND AN INVERSE SCATTERING FORMULATION OF THE SAS EINSTEIN-MAXWELL FIELD-EQUATIONS
ERIS, A; GURSES, M; Karasu, Atalay (AIP Publishing, 1984-01-01)
We formulate stationary axially symmetric (SAS) Einstein–Maxwell fields in the framework of harmonic mappings of Riemannian manifolds and show that the configuration space of the fields is a symmetric space. This result enables us to embed the configuration space into an eight‐dimensional flat manifold and formulate SAS Einstein–Maxwell fields as a σ‐model. We then give, in a coordinate free way, a Belinskii–Zakharov type of an inverse scattering transform technique for the field equations supplemented by a...
A new integrable generalization of the Korteweg-de Vries equation
Karasu-Kalkanli, Ayse; Karasu, Atalay; Sakovich, Anton; Sakovich, Sergei; TURHAN, REFİK (AIP Publishing, 2008-07-01)
A new integrable sixth-order nonlinear wave equation is discovered by means of the Painleve analysis, which is equivalent to the Korteweg-de Vries equation with a source. A Lax representation and an auto-Backlund transformation are found for the new equation, and its traveling wave solutions and generalized symmetries are studied. (C) 2008 American Institute of Physics.
Exact solutions for vibrational levels of the Morse potential
Taşeli, Hasan (IOP Publishing, 1998-01-16)
The vibrational levels of diatomic molecules via Morse potentials are studied by means of the system confined in a spherical box of radius l, II is shown that there exists a critical radius l(cr),, at which the spectrum of the usual unbounded system can be calculated to any desired accuracy. The results are compared with those of Morse's classical solution which is based on the assumption that the domain of the internuclear distance r includes the unphysical region (-infinity, 0). By determining numerically...
Hydrodynamic type integrable equations on a segment and a half-line
Guerses, Metin; Habibullin, Ismagil; Zheltukhın, Kostyantyn (AIP Publishing, 2008-10-01)
The concept of integrable boundary conditions is applied to hydrodynamic type systems. Examples of such boundary conditions for dispersionless Toda systems are obtained. The close relation of integrable boundary conditions with integrable reductions in multifield systems is observed. The problem of consistency of boundary conditions with the Hamiltonian formulation is discussed. Examples of Hamiltonian integrable hydrodynamic type systems on a segment and a semiline are presented. (C) 2008 American Institut...
Symmetry reductions of a Hamilton-Jacobi-Bellman equation arising in financial mathematics
Naicker, V; Andriopoulos, K; Leach, PGL (Informa UK Limited, 2005-05-01)
We determine the solutions of a nonlinear Hamilton-Jacobi-Bellman equation which arises in the modelling of mean-variance hedging subject to a terminal condition. Firstly we establish those forms of the equation which admit the maximal number of Lie point symmetries and then examine each in turn. We show that the Lie method is only suitable for an equation of maximal symmetry. We indicate the applicability of the method to cases in which the parametric function depends also upon the time.
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
S. Kondo and T. Watari, “String-Theory Realization of Modular Forms for Elliptic Curves with Complex Multiplication,”
COMMUNICATIONS IN MATHEMATICAL PHYSICS
, pp. 89–126, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/66167.