## C. Douglas Haessig

Assistant Professor, Mathematics

Ph.D., University of California, Irvine, 2005

B.S., University of California, Santa Barbara, 1998

**Research Summary**

A large part of my research consists of studying families of exponential sums over finite fields. My approach mostly uses techniuqes of p-adic analysis, pioneered by Bernard Dwork in the 1960s.

**Selected Publications**

Haessig and Sperber. *L-functions associated with families of toric exponential sums*

Haessig and Rojas-Leon. *L-functions of symmetric powers of the generalized Airy family of exponential sums: ell-adic and p-adic methods.*

Haessig, On the zeta function of divisors of projective varieties with large rank divisor class group, J. Number Theory. Vol 129, Issue 5, May 2009, Pages 1161-1177

Haessig, L-functions of symmetric powers of cubic exponential sums. J. Reine Angew. Vol 2009, Issue 631, Pages 1 - 57

Haessig. On the p-adic meromorphy of the function field height zeta function. J. Number Theory (2007) Vol 128/7, pp. 2063-2069.

Haessig. Equalities, congruences, and quotients of zeta functions in Arithmetic Mirror Symmetry. Appendix to D. Wan's Mirror symmetry for zeta functions. Mirror Symmetry V, AMS/IP Studies in Advanced Mathematics, Vol. 38, (2007) 159-184.

D. Wan and C. D. Haessig. On the p-adic Riemann hypothesis for the zeta function of divisors. J. Number Theory. 104 (2004) 335-352.

**Expositions**

Haessig. Exponentials sums and the Chevalley-Warning theorem (Michigan number theory days. 2010)

**Courses**

2014 (S) 236H: Algebra (Homework)

2014 (S) Complex Analysis (Syllabus and Homework)

2013 (S) Topics Course II (Course Notes)

2012 (F) Topics Course (Course Notes)

2010 (F) Math 436 (Syllabus)

2010 (S) Math 130 (Syllabus) and Math 285 (Syllabus)

2009 (F) Math 141, 163 and Topics in Number theory

2009 (S) Math 200, 235

2008 (F) Math 233

2008 (S) Math 141A, 282

2007 (F) Math 162Q, 230

2007 (S) Math 142, 236

2006 (F) Math 141, 230

**Opportunities for Undergraduates and Graduates**

Fellowships - UR database

**Past Student Projects**

- Tim McCrossen (S10): An Introduction to Separation of Variables with Fourier Series, Fourier1.nb, Fourier2.nb, Fourier3.nb
- Corey Adams (S10): Special Relativity and Linear Algebras
- Kevin Tang (S10): Newton's method in Mathematica, Newton animation
- James Grotke (S10): An Introduction to the Mathematics of Value-at-Risk
- Jaime Sorenson:
- Elizabeth Munch: The Ihara zeta function for graphs and 3-adic convergence of the Sierpinski gasket
- Alex Halperin: Complex Multiplication: Kronecker's Jugendtraum for Q(i)
- Max Mikel-Stites: An overview of general encryption techniques with a focus on asymmetric key encryption
- Diane Panagiotopoulos: The mathematics of juggling
- Max Abernethy: RSA techniques
- Michael Weiss: Sylow Theorems