# REU 1999: The Igusa Local Zeta Function and Elliptic Curves (M. Robinson)

From left, back: Mark Peterson, Lubomira Ivanova, Kim Schneider,
Michael Joyce, Jason Slemons, Emily Clark, Aaron Koll. From left,
front: Anushka Krishnachander, Jenny Ross, Mariana Campbell, Yanir
Rubinstein, Ed Dubois, Margaret Robinson.

The student participants in the number theory group were:
- Mariana Campbell (UC San Diego '00), University of Pennsylvania
- Ed DuBois (Pomona '00),
- Michael Joyce (Tulane '00), Brown University
- Anushka Krishnachander (Amherst '01)
- Kim Schneider (Bowdoin '00), Penn State University
- Jason Slemons (UC Berkeley '00), University of Washington

The group produced the following preliminary report which computes the Igusa local zeta function for six of the eight reduction types given by the Kodaira-Neron classification of an elliptic curve :

- The Igusa local
zeta function for the different reduction types of the special
fiber of an elliptic curve

The following paper by Diane Meuser and Margaret Robinson published in Mathematics of Computation cites the work of the 1999 REU group and completes the calculation of the Igusa local zeta function for the two infinite families of elliptic curve in the Kodaira-Neron Classification:

- The Igusa local
zeta functions of an elliptic curve, Math. Comp., 71 (2001), no. 238, 815-823.

** Abstract: **
We determine the explicit form of the Igusa local zeta function
associated to an elliptic curve. The denominator is known to be
trivial. Here we determine the possible numerators and classify them
according to the Kodaira-Neron classification of the special
fibers of elliptic curves as determined by Tate's algorithm.

[ REU home page ]
[ List
of REU projects since 1988 ]
[ M. Robinson's home page ]