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A set of nonlinear differential equations associated with the Eisenstein series of the congruent subgroup Î“0(2) of the modular group SL2(Z) is constructed. These nonlinear equations are analogues ofâ€¦ (More)

- Heekyoung Hahn
- 2006

In this paper, we define three normalized Eisenstein series P , e, and Q associated with Î“0(2), and derive three differntial equations satisfied by them by using some trigonometirc identities. Byâ€¦ (More)

- Heekyoung Hahn
- 2006

Let Î“ â‰¤ SL2(R) be a genus zero Fuchsian group of the first kind with âˆž as a cusp, and let E 2k be the holomorphic Eisenstein series of weight 2k on Î“ that is nonvanishing at âˆž and vanishes at all theâ€¦ (More)

- Heekyoung Hahn
- 2006

One of the main goals in this paper is to establish convolution sums of functions for the divisor sums ÏƒÌƒs(n) = âˆ‘ d|n(âˆ’1)d and ÏƒÌ‚s(n) = âˆ‘ d|n(âˆ’1) n d d, for certain s, which were first defined byâ€¦ (More)

- R. C. Gupta, J. G. Cottingham, +19 authors E. Willen
- Conference Record of the 1991 IEEE Particleâ€¦
- 1991

The Relativistic Heavy Ion Collider (RHIC) has six interaction regions for the colliding beam. Each interaction region is part of an insertion region consisting of several magnets. The requiredâ€¦ (More)

- P. A. Thompson, R. C. Gupta, +4 authors E. Willen
- Conference Record of the 1991 IEEE Particleâ€¦
- 1991

Using the experience gained in designing and building Relativistic Heavy Ion Collider (RHIC) dipole prototype magnets, an improved cross section has been developed. Significant features of thisâ€¦ (More)

- P. A. Thompson, R. C. Gupta, +4 authors E. Willen
- Conference Record of the 1991 IEEE Particleâ€¦
- 1991

The Relativistic Heavy Ion Collider (RHIC) will require 360 dipoles of 80 mm bore. The authors discuss the field perturbations produced by the saturation of the yoke iron. Changes have been made toâ€¦ (More)

- R. Gomez-Escoto, Mohammed Ghafari, Branko Stahl, Heekyoung Hahn
- IEEE International Magnetics Conference
- 1999

In the present paper we repon on the magnetic and electrical properties of discontinuous granular thin films. The granular thin films consisting of ultrafine metallic particles and oxides show a spinâ€¦ (More)

- G. F. Dell, Heekyoung Hahn, S. Y. Lee, George Parzen, Steven Tepikian
- Conference Record of the 1991 IEEE Particleâ€¦
- 1991

The correction scheme for skew-quadrupole (a/sub 1/) errors in the Relativistic Heavy Ion Collider is presented. The a/sub 1/ errors result from fabrication and from installation errors. At theâ€¦ (More)

- Jie Wei, Mike Blaskiewicz, +12 authors S. Kurennoy
- 2002

where r0 is the classical radius of proton, R0 is the average radius of circumference, Î½x,y,0 and Ïƒx,y are the base transverse tunes and rms beam sizes, and fsc (1/2 for an uniform, 1 for a Gaussianâ€¦ (More)