Elliptic Curves Arising from the Spectral Zeta Function for Non-Commutative Harmonic Oscillators and Γ0(4)-Modular Forms

2006 ◽  
pp. 201-218 ◽  
Author(s):  
K. KIMOTO ◽  
M. WAKAYAMA
Keyword(s):  
Zeta Function ◽  
Elliptic Curves ◽  
Modular Forms ◽  
Harmonic Oscillators ◽  
Spectral Zeta Function

VACUUM ENERGY IN SPHERICAL DOMAINS: WKB AND UNIFORM ASYMPTOTIC EXPANSIONS

1996 ◽  
Vol 11 (22) ◽  
pp. 4129-4146 ◽  
Author(s):  
AUGUST ROMEO
Keyword(s):  
Zeta Function ◽  
Asymptotic Expansions ◽  
Zero Point ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Point Energy ◽  
Dimensional Dependence ◽  
Spherical Domains ◽  
Spectral Zeta Function ◽  
Uniform Asymptotic Expansions

We evaluate the finite part of the regularized zero-point energy for a massless scalar field confined in the interior of a D-dimensional spherical region. While some insight is offered into the dimensional dependence of the WKB approximations by examining the residues of the spectral-zeta-function poles, a mode-sum technique based on an integral representation of the Bessel spectral zeta function is applied with the help of uniform asymptotic expansions (u.a.e.’s).

scholarly journals Quasi-modular forms attached to elliptic curves, I

2012 ◽  
Vol 19 (2) ◽  
pp. 307-377 ◽  
Author(s):  
Hossein Movasati
Keyword(s):  
Elliptic Curves ◽  
Modular Forms

scholarly journals Higher reciprocity law, modular forms of weight 1 and elliptic curves

1985 ◽  
Vol 98 ◽  
pp. 109-115 ◽  
Author(s):  
Masao Koike
Keyword(s):  
Elliptic Curves ◽  
Modular Forms ◽  
Cusp Forms ◽  
Close Connection ◽  
Irreducible Polynomials ◽  
Reciprocity Law

In this paper, we study higher reciprocity law of irreducible polynomials f(x) over Q of degree 3, especially, its close connection with elliptic curves rational over Q and cusp forms of weight 1. These topics were already studied separately in a special example by Chowla-Cowles [1] and Hiramatsu [2]. Here we bring these objects into unity.

scholarly journals Elliptic curves, modular forms, and sums of Hurwitz class numbers

2008 ◽  
Vol 128 (6) ◽  
pp. 1847-1863 ◽  
Author(s):  
Brittany Brown ◽  
Neil J. Calkin ◽  
Timothy B. Flowers ◽  
Kevin James ◽  
Ethan Smith ◽  
...  
Keyword(s):  
Elliptic Curves ◽  
Modular Forms ◽  
Class Numbers
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