Mathematics Department

C D Haessig

C. Douglas Haessig

Assistant Professor, Mathematics
Ph.D., University of California, Irvine, 2005
B.S., University of California, Santa Barbara, 1998

CV | Seminars

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. p-adic unit roots of L-functions over finite fields

Haessig. Meromorphy of the rank one unit root L-function revisited, Finite Fields Appl. 30 (2014), 191–202.

Haessig and Sperber. Families of generalized Kloosterman sums

Haessig and Sperber. L-functions associated with families of toric exponential sums, J. Number Theory 144 (2014), 422–473.

Haessig and Rojas-Leon. L-functions of symmetric powers of the generalized Airy family of exponential sums: ell-adic and p-adic methods., Int. J. Number Theory 7 (2011), no. 8, 2019–2064.

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

   2015 (S) Topics course
   2014 (F) Math 164, 265
   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