# Eisenstein's footnote

## Related Articles

- Gauss, Eisenstein, and the "Third" Proof of the Quadratic Reciprocity Theorem: Ein kleines Schauspiel. Laubenbacher, Reinhard C.; Pengelley, David J. // Mathematical Intelligencer;Spring94, Vol. 16 Issue 2, p67
Presents the work of mathematicians Gotthold Eisenstein and Carl Freidrich Gauss to the quadratic reciprocity theorem. Importance of the theorem; Gauss's lemma; Mathematicians' account of the work.

- An algorithm for calculating the roots of a general quintic equation from its coefficients. King, R. B.; Canfield, E. R. // Journal of Mathematical Physics;Apr91, Vol. 32 Issue 4, p823
Classical mathematics is used to derive an algorithm for expressing the roots of a general quintic equation in terms of its coefficients. This algorithm requires the solution of two quadratic equations and one cubic equation as well as the evaluation of two infinite series, namely, one Jacobi...

- quintic. // Hutchinson Dictionary of Scientific Biography;2005, p1
To the power of five.

- On the Relationship Between the Wigner-Moyal and Bohm Approaches to Quantum Mechanics: A Step to a More General Theory? Hiley, B. J. // Foundations of Physics;Apr2010, Vol. 40 Issue 4, p356
In this paper we show that the three main equations used by Bohm in his approach to quantum mechanics are already contained in the earlier paper by Moyal which forms the basis for what is known as the Wigner-Moyal approach. This shows, contrary to the usual perception, that there is a deep...

- Patterns due to quintic kinetics in a diffusion-reaction system with global interaction. Sheintuch, Moshe; Nekhamkina, Olga // Journal of Chemical Physics;12/22/1998, Vol. 109 Issue 24, p10612
Investigates the quintic kinetics in a diffusion-reaction system. Behavior of electrochemical oscillations; Effect of catalyst interaction with a mixed fluid phase on global interaction; Features of the quintic model simulation.

- Stability of negative solitary waves for an integrable modified Camassaâ€“Holm equation. Jiuli Yin; Lixin Tian; Xinghua Fan // Journal of Mathematical Physics;May2010, Vol. 51 Issue 5, p053515
In this paper, we prove that the modified Camassaâ€“Holm equation is PainlevÃ© integrable. We also study the orbital stability problem of negative solitary waves for this integrable equation. It is shown that the negative solitary waves are stable for arbitrary wave speed of propagation.

- Standing Ring Blow up Solutions to the N-Dimensional Quintic Nonlinear Schrï¿½dinger Equation. Rapha�l, Pierre; Szeftel, J�r�mie // Communications in Mathematical Physics;Sep2009, Vol. 290 Issue 3, p973
We consider the quintic nonlinear Schrï¿½dinger equation $${i\partial_tu=-\Delta u-|u|^{4}u}$$ in dimension N = 3. This problem is energy critical in dimension N = 3 and energy super critical for N = 4. We prove the existence of a radially symmetric blow up mechanism with L2 concentration...

- LINEAR ESTIMATE OF THE NUMBER OF ZEROS OF ABELIAN INTEGRALS FOR A KIND OF QUINTIC HAMILTONIANS. Nyamoradi, N.; Zangeneh, H. R. Z. // Bulletin of the Iranian Mathematical Society;Jul2011, Vol. 37 Issue 2, p101
We consider the number of zeros of the integral I(h) = Ï•Î“h Ï‰ of real polynomial form ! of degree not greater than n over a family of vanishing cycles on curves Î“h : y2 + 3x2 - x6 = h, where the integral is considered as a function of the parameter h. We prove that the number of...

- Landauï¿½Ginzburg/Calabiï¿½Yau correspondence for quintic three-folds via symplectic transformations. Chiodo, Alessandro; Yongbin Ruan // Inventiones Mathematicae;Nov2010, Vol. 182 Issue 1, p117
We compute the recently introduced Fanï¿½Jarvisï¿½Ruanï¿½Witten theory of W-curves in genus zero for quintic polynomials in five variables and we show that it matches the Gromovï¿½Witten genus-zero theory of the quintic three-fold via a symplectic transformation. More specifically,...