Caroline TurnageButterbaugh
William W. Elliott Assistant Research Professor
Current Research Interests
analytic and algebraic number theory, including properties of the Riemann zetafunction and Lfunctions, zeros of Lfunctions, and class groups of number fields
Current Appointments & Affiliations
 William W. Elliott Assistant Research Professor, Mathematics, Trinity College of Arts & Sciences 2015  2018
 Assistant Research Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2015
Contact Information
 Background

Education, Training, & Certifications
 Ph.D., University of Mississippi 2014

Academic Positions Outside Duke
 Postdoctoral Researcher, MSRI. 2017
 Postdoctoral Research Fellow, North Dakota State University. 2014  2015
 Postdoctoral Undergraduate Research Mentor, Williams College. 2014
 Recognition

In the News

OCT 24, 2017 fivethirtyeight.com


Awards & Honors
 Postdoctoral Fellow. MSRI. 2017
 University of Mississippi Class Marshal. University of Mississippi Graduate School . 2014
 Graduate Instructor Excellence in Teaching Award. University of Mississippi Graduate School . 2013
 Graduate Student Achievement Award in Mathematics. University of Mississippi Graduate School . 2013
 GAANN 5 year fellowship. University of Mississippi, Department of Mathematics. 2009
 Research

Selected Grants
 Re:boot Number Theory awarded by National Security Agency 2016  2018

Fellowships, Supported Research, & Other Grants
 Visiting scientist awarded by Max Planck Institute of Mathematics 2018
 Mathematics travel grant awarded by AWM/NSF 2014
 Summer Research Grant awarded by GAANN 2013
 Summer Research Grant awarded by GAANN 2012
 Summer Research Grant awarded by GAANN 2010
 Publications & Artistic Works

Selected Publications

Book Sections
 Mackall, B, Miller, SJ, Rapti, C, TurnageButterbaugh, C, and Winsor, K. "Some Results in the Theory of Lowlying Zeros." In Families of Automorphic Forms and the Trace Formula. Springer, September 20, 2016. (Chapter)
 Barrett, O, Firk, F, Miller, SJ, and TurnageButterbaugh, C. "From Quantum Systems to LFunctions: Pair Correlation Statistics and Beyond." In Open Problems in Mathematics, 123171. Springer, August 6, 2016. (Chapter)
 Edelsbrunner, X, Huan, K, Mackall, B, Powell, J, TurnageButterbaugh, C, and Weinstein, M. "Benfordness of the Cauchy Distribution and Generalizations." In Benford's Law Theory and Applications. Princeton University Press, June 9, 2015. (Appendix)

Journal Articles
 Conrey, JB, and TurnageButterbaugh, CL. "On rgaps between zeros of the Riemann zetafunction (Accepted)." Bulletin of the London Mathematical Society (January 1, 2018). Full Text
 Best, A, Dynes, P, Edelsbrunner, X, McDonald, B, Miller, SJ, Tor, K, TurnageButterbaugh, C, and Weinstein, M. "Benford Behavior of Generalized Zeckendorf Decompositions." Springer Proceedings in Mathematics and Statistics 220 (January 1, 2017): 2537. Full Text
 Pierce, LB, TurnageButterbaugh, CL, and Wood, MM. "An effective Chebotarev density theorem for families of number fields, with an application to $\ell$torsion in class groups." (submitted) (2017). Link to Item
 Bui, HM, Heap, WP, and TurnageButterbaugh, CL. "GAPS BETWEEN ZEROS OF DEDEKIND ZETAFUNCTIONS OF QUADRATIC NUMBER FIELDS. II." The Quarterly Journal of Mathematics 67, no. 3 (September 1, 2016): 467482. Full Text
 Best, A, Dynes, P, Edelsbrunner, X, McDonald, B, Miller, SJ, Tor, K, TurnageButterbaugh, C, and Weinstein, M. "Gaussian distribution of the number of summands in generalized Zeckendorf decomposition in small intervals." Integers 16 (2016).
 Barrett, O, McDonald, B, Miller, SJ, Ryan, P, TurnageButterbaugh, CL, and Winsor, K. "Gaps between zeros of GL(2) Lfunctions." Journal of Mathematical Analysis and Applications 429, no. 1 (September 2015): 204232. Full Text
 Banks, WD, Freiberg, T, and TurnageButterbaugh, CL. "Consecutive primes in tuples." Acta Arithmetica 167, no. 3 (2015): 261266. Full Text
 TurnageButterbaugh, CL. "Gaps between zeros of Dedekind zetafunctions of quadratic number fields." Journal of Mathematical Analysis and Applications 418, no. 1 (October 2014): 100107. Full Text
 Milinovich, MB, and TurnageButterbaugh, CL. "Moments of products of automorphic Lfunctions." Journal of Number Theory 139 (June 2014): 175204. Full Text
 Best, A, Dynes, P, Edelsbrunner, X, McDonald, B, Miller, SJ, Tor, K, TurnageButterbaugh, C, and Weinstein, M. "Benford behavior of Zeckendorf decompositions." Fibonacci Quarterly 52, no. 5 (2014): 3546.
 Best, A, Dynes, P, Edelsbrunner, X, McDonald, B, Miller, SJ, Tor, K, Weinstein, M, and TurnageButterbaugh, C. "Gaussian behavior of the number of summands in Zeckendorf decompositions in small intervals." Fibonacci Quarterly 52, no. 5 (2014): 4753.

 Teaching & Mentoring

Recent Courses
 Scholarly, Clinical, & Service Activities

Presentations & Appearances
 An effective Chebotarev density theorem for families of number fields. Algebra, Geometry, and Number Theory Seminar. Tufts University. November 2017 2017
 Gaps between zeros of the Riemann zetafunction. Department Colloquium. Oberlin College. November 2017 2017
 Bounded gaps between primes. Department Colloquium. Elon University. October 2017 2017
 An effective Chebotarev density theorem for families of number fields. Algebraic Geometry and Number Theory Seminar. Rice University. April 2017 2017
 Bounding ltorsion in class groups. AMS Special Session on Analytic Number Theory and Automorphic Forms. Washington State University . April 2017 2017
 An effective Chebotarev density theorem for families of number fields. Connections for Women, Analytic Number Theory Workshop. MSRI. January 2017 2017
 On rgaps between zeros of the Riemann zetafunction. AMS Special Session on Analytic Number Theory and Arithmetic. Joint Mathematics Meetings. January 2017 2017
 Investigating the vertical distribution of zeros of Lfunctions. Computational aspects of Lfunctions. ICERM. November 2015 2015
 Gaps between zeros of Lfunctions. Elementary, analytic, and algorithmic number theory: Research inspired by the mathematics of Carl Pomerance. University of Georgia. June 2015 2015
 Moments of Lfunctions and applications. ENFANT (Exciting New Faces in Analytic Number Theory). Hausdorff Center for Mathematics. July 2014 2014

Outreach & Engaged Scholarship
 SWIM (Summer Workshop in Mathematics). Course Instructor. Duke University Department of Mathematics. June 2017 2017
 SCUWM (Southeastern Conference for Undergraduate Women in Mathematics). Speaker. Duke University Department of Mathematics. November 2016  November 2016 2016
 Harkness Table Series. Invited Speaker. Spartanburg Day School. October 2016 2016

Service to the Profession
 coorganizer . Advances in algebraic and analytic number theory. MCA. July 2017 2017
 codirector. re:boot Number Theory 2017. Duke University. June 2017 2017
 coorganizer. Lfunctions and other animals. MAA. January 2017 2017
 codirector. re:boot Number Theory 2016. Duke University . March 2016 2016
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