Derived periods and the Mazur-Tate circle pairing

Developped by Massimo Bertolini and Henri Darmon.

To run the Circle pairing programs you should have a machine with PARI/GP (v.2.1.1 or higher) already installed, preferably running Linux or Unix.

1. Downloading

1. Download the file MTcircle. This is a regular ASCII file containing a collection of PARI routines, and a sample script, for running the calculations that were performed to test the conjectures in

[BD] M. Bertolini and H. Darmon, A Birch and Swinnerton-Dyer conjecture for the Mazur-Tate circle pairing, manuscript, in progress.

2. From the directory where you have saved the file MTcircle, invoke PARI by typing


from the UNIX command prompt.

From the PARI prompt type

\r MTcircle

This will launch PARI into a sequence of calculations whose end result is to verify the BSD conjecture for the Mazur-Tate circle pairing in a special case (the curve of conductor 61 denoted 61A in Cremona's tables, over the real quadratic field of discriminant 5) to an accuracy of 12 decimal digits.

2. Using the circle pairing package

The file MTcircle contains comments to help the user in understanding how to use the various routines it contains. Feel free to modify the programs and experiment on other inputs. If you find any mistakes in the programs (or, a counterexanple to the conjecture of [BD]) please send me an email!