Sharon M. Frechette

Assistant Professor

		Email:	sfrechet@mathcs.holycross.edu
		US Mail:	Department of Mathematics & Computer Science College of the Holy Cross 1 College Street Worcester, MA 01610
		Office:	Swords 321
		Phone:	(508) 793-2257
		Fax:	(508) 793-3040
		Availability:	Click here for current schedule.

TEACHING

EDUCATION

• Ph.D., Dartmouth College, 1997.
  Advisor: Thomas Shemanske.
  Thesis: "Decomposition of Spaces of Half-Integral Weight Cusp Forms".

• A.M.,Dartmouth College, 1994.

• B.A., Boston University, 1988.
  Senior Thesis Advisor: Paul Blanchard.
  

RESEARCH INTERESTS

• Number Theory: Specifically modular forms of integral and half-integral weight, the Shimura correspondence, special values of L-functions, the connection between modular forms and elliptic curves, and Gaussian hypergeometric functions as related to traces of Hecke operators.

PUBLICATIONS

• "Nonvanishing of Special Values of $L$-functions for Quadratic Twists of Newforms," preprint.
• " An Interdisciplinary Course: 'On Beauty: Perspective, Proportion, and Rationalism in Western Culture,' (with Alison Fleming and Sarah Luria), refereed Conference Proceedings for Renaissance Banff: Mathematical Connections in Art, Music, and Science (July 2005), accepted for publication, 4 pages.
• "Determinants Associated to Zeta Matrices of Posets," (with Cristina Ballantine and John Little), Linear Algebra Appl., 411C (2005), 364-370.   [Preprint version]
• "Nonvanishing Twists of $GL(2)$ Automorphic $L$-functions," (with Alina Bucur, Ben Brubaker, Gautam Chinta, and Jeffrey Hoffstein), Internat. Math. Res. Notices, 78 (2004), 4211-4239.   [Preprint version]
• "The Combinatorics of Traces of Hecke Operators," (with Ken Ono and Matthew Papanikolas), Proc. of the National Academy of Sciences, USA, 101 (2004), 17016-17020.   [Preprint version]
• "Gaussian Hypergeometric Functions and Traces of Hecke Operators," (with Ken Ono and Matthew Papanikolas), Internat. Math. Res. Notices, 60 (2004), 3233-3262.  [Preprint version]
• "A Classical Characterization of Newforms with Equivalent Eigenforms in S_{k + 1/2}(4N,\chi)," J. London Math. Soc., (3) 68 (2003), 563--578.   [Preprint version]
• "Hecke Structure of Spaces of Half-Integral Weight Cusp Forms," Nagoya Math. J., 159 (2000), 53--85.   [Preprint version]

CONFERENCES

I was one of the co-organizers for the 18th Annual Workshop on Automorphic Forms and Related Topics, which was held March 21-24, 2004 at the University of California, Santa Barbara.

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Created by Sharon M. Frechette on Jan. 24, 2004
Last modified by Sharon M. Frechette on September 12, 2006