From Lemniscate to Langlands

Web excerpts compiled by
Steven H. Cullinane on January 17, 2004

From
The Experimental Mathematician:
The Pleasure of Discovery and the Role of Proof,
by Jonathan M. Borwein --

From
N. H. Abel on Elliptic Functions:
Problems of Division and Reduction,
by Henrik Kragh SØrensen --

Also from SØrensen --

From
Algebraic Symmetries I,
Fall 1999 Lectures on
The Practice of Mathematics
by Robert P. Langlands --

After Gauss and before Langlands came, of course, Abel.

For an excellent account of how Abel followed up Gauss's hint on the lemniscate, see Henrik Kragh SØrensen's

Niels Henrik Abel and the Theory of Equations.

Related material --

Arithmetic-Geometric Mean (MathWorld)

Gauss's Constant (MathWorld)

Lemniscate (MathWorld)

Lemniscate Function (MathWorld)

Lemniscate Constant (MathWorld)

Gauss's Lemniscate Constant (Mathsoft)

Gauss's Lemniscate Constant References (Mathsoft)

Elliptic Curves and Modular Forms (A Classical Introduction)

"Abel's Theorem on the Lemniscate," by Michael Rosen,
American Mathematical Monthly 88 (1981) No. 6, 387-395

 Page created Jan. 17, 2004