Caroline Turnage-Butterbaugh
Associate Professor of Mathematics,
Mathematics and Statistics
Associate Professor of Mathematics and Statistics, Mathematics and Statistics
Associate Professor of Mathematics and Statistics, Mathematics and Statistics
Education & Professional History
Wofford College, BA; Wake Forest University, MA; University of Mississippi, PhD
Current Funding
- NSF CAREER DMS-2239681 (2023-2029, PI)
Previous Appointments
- William W. Elliott Assistant Research Professor, Duke University, 2015-2018
- Postdoctoral Fellow, Mathematical Sciences Research Institute, Spring 2017
- Postdoctoral Research Fellow, North Dakota State University, 2014-2015
- Postdoctoral Undergraduate Research Mentor, Williams College, Summer 2014
At Carleton since 2018.
Research Interests
My research interests lie in the field of analytic number theory. In particular, I study properties of L-functions (such as the Riemann zeta-function, Dedekind zeta-functions, Artin L-functions, and automorphic L-functions), their zeros, and class groups of number fields.
My work is partially supported by the National Science Foundation under grant NSF CAREER DMS-2239681. It was previously supported by NSF DMS-1902193 (2019-2023, PI) and NSF FRG DMS-1854398 (2019-2023, Senior Scientist Consultant).
Research Related Travel & Talks
2026
- Joint Mathematics Meetings
January 4-7, 2026
Washington Convention Center
Washington, D.C.
2025
- AIM Workshop: Moments of the Derivative of Characteristic Polynomials and L-functions (co-organizer)
December 1 – 5, 2025
American Institute of Mathematics
Pasadena, CA - Integers Conference (plenary speaker)
A conference in honor of the 80th birthdays of Melvyn Nathanson and Carl Pomerance
May 14 – 17, 2025
University of Georgia
Athens, Georgia
2024
- Reverse Site Visit
October 8, 2024
National Science Foundation
Alexandria, VA - Analytic Number Theory and Arithmetic Statistics
A conference celebrating the mathematical contributions of Chantal David
August 26-30, 2024
Centre de recherches mathématiques
Montréal, Québec, Canada
- International Conference on L-functions and Automorphic Forms
May 13-16, 2024
Vanderbilt University
Nashville, TN
- Number Theory Seminar
April 17, 2024
Kansas State University
Manhattan, KS
- Analytic Number Theory
March 10-19, 2024
Institut Mittag-Leffler
Djursholm, Sweden
2023
- Number Theory Seminar & Department of Mathematics Colloquium
November 28 & 30, 2023
University of Illinois Urbana-Champaign
Urbana, IL
- Department of Mathematics Colloquium
November 16, 2023
Vanderbilt University
Nashville, TN
- AWM Career Panel (invited panelist)
November 10, 2023
Syracuse University (virtual)
- PIMS Network Wide Graduate Courses (guest lecturer)
November 9, 2023
MATH 740: Moments of L-functions, Instructor: Alia Hamieh (UNBC)
(virtual)
- Joint Athens-Atlanta Number Theory Seminar
October 24, 2023
Georgia Institute of Technology
Atlanta, GA
- AIM Workshop: Delta Symbols and the Subconvexity Problem
October 16-20, 2023
American Institute of Mathematics
Pasadena, CA
- AMS Special Session on Analytic Number Theory and Related Fields
October 7-8, 2023
2023 Fall Central Sectional Meeting, Creighton University
Omaha, NE
- Arithmetic, Algebra, and Algorithms (invited participant)
April 10-14, 2023
International Centre for Mathematical Sciences
Edinburgh, Scotland
- Algebra/Number Theory Seminar
March 15, 2023
University of Rochester
Rochester, NY
2022
- Number Theory Seminar
December 7 , 2022
Duke University
Durham, NC
- Number Theory Days
September 30 – October 1, 2022
École Polytechnique Fédérale de Lausanne
Lausanne, Switzerland - Focused Research Group (FRG) Graduate Seminar
September 22, 2022
American Institute of Mathematics (Virtual)
- Duke University (research visit)
September 2, 2022
Durham, NC
- American Institute of Mathematics (FRG research visit)
August 8-12, 2022
San Jose, California
- ANTeater ’22
August 1-4, 2022
University of California – Irvine
Irvine, California
- PRiME Colloquium
July 22, 2022
Pomona College (Virtual)
- PIMS CRG Workshop on Moments of L-functions
July 25-29, 2022
University of Northern British Columbia
Prince George, BC, Canada (Virtual)
- 50 Years of Number Theory & Random Matrix Theory Conference (invited participant)
June 21-24, 2022
Institute for Advanced Study
Princeton, New Jersey
- AWM Research Symposium Special Session: Number Theory (co-organizer)
June 16-19, 2022
The Institute for Mathematics and its Applications, University of Minnesota
Minneapolis, Minnesota
- 47th Annual New York Regional Graduate Mathematics Conference (plenary speaker)
April 2-3, 2022
Syracuse University
Syracuse, New York - American Institute of Mathematics (FRG research visit)
February 3 – March 25, 2022
San Jose, California
2021
- Algebraic Geometry and Number Theory Seminar
October 20, 2021
Chalmers University of Technology / University of Gothenburg (Virtual) - Focused Research Group (FRG) Graduate Seminar
October 4, 2021
American Institute of Mathematics (Virtual)
- American Institute of Mathematics (FRG research visit)
August 18 – 31, 2021
San Jose, California
- Wofford College Summer Research Seminar
June 28, 2021
Spartanburg, South Carolina
- Vanderbilt Number Theory Seminar
May 5, 2021
Vanderbilt University (Virtual)
- Quebec-Vermont Number Theory Seminar
April 29, 2021
Université de Montréal (Virtual)
- UVA Number Theory Seminar
April 23, 2021
University of Virginia (Virtual)
- Purdue Analytic Number Theory and Harmonic Analysis seminar (PANTHA)
March 31, 2021
Purdue University (Virtual) - Focused Research Group (FRG) Seminar
March 16, 2021
American Institute of Mathematics (Virtual)
- KSU Number Theory Seminar
March 8, 2021
Kansas State University (Virtual)
- Virtual Brazilian Number Theory Seminar (ViBraNT)
February 25, 2021
Universidade Federal de Minas Gerais, Brazil (Virtual)
- UM Algebra and Number Theory Seminar
February 4, 2021
University of Mississippi (Virtual)
2020
- Automorphic Forms and Arithmetic
August 30 – September 5, 2020
Mathematisches Forschungsinstitut Oberwolfach, Germany (Virtual)
- MathFest (Project NExT Fellow)
July 28 – August 1, 2020
Philadelphia, PA (Virtual)
- VaNTAGeSeminar
Tuesday, February 18, 2020
Broadcasting live from Northfield, MN!
- Joint Mathematics Meetings (invited speaker and Project NExT fellow)
January 15-18, 2020
Denver, CO
2019
- Duke University(research visit)
December 11-20, 2019
Durham, NC
- Analytic Number Theory
November 3 – 9, 2019
Mathematisches Forschungsinstitut Oberwolfach, Germany
- American Institute of Mathematics (FRG research visit)
August 27 – September 4, 2020
San Jose, CA
- MathFest(Project NExT Fellow)
July 31 – August 3, 2019
Cincinnati, Ohio
- NSF-CBMS Conference: L-functions and Multiplicative Number Theory(invited speaker)
University of Mississippi, May 20-24, 2019
Oxford, Mississippi
- Analytic Aspects of Automorphic Forms (invited speaker)
Université de Lille, April 3-5, 2019
Lille, France
- Value Distribution of Zeta and L-functions and Related Topics (invited speaker)
RIKEN Institute March 21 – 27, 2019
Wako, Japan
2018
- CMS 2018 Winter Meeting
Special Session: Distributions in Analytic Number Theory
Vancouver, Canada
December 7 – 10, 2018
- University of Minnesota – Number Theory Seminar
Minneapolis, MN
December 3, 2018
- LMS-CMI Research School: New Trends in Analytic Number Theory
Exeter, United Kingdom
August 13 – 17, 2018
slides
- Max Planck Institute for Mathematics (research visit)
Bonn, Germany
July 1 – 31, 2018
• Number Theory Lunch Seminar (July 18, 2018)
• PLeaSANT Seminar (July 25, 2018) - Number Theory Seminar
Mathematical Institute, University of Cologne
Cologne, Germany
July 10, 2018 - HCM School: L-functions: Open Problems and Current Methods (course lecturer)
Bonn, Germany
June 25 – 29, 2018 - Perspectives on the Riemann Hypothesis
Bristol, United Kingdom
June 4 – 7, 2018 - Institute for Advanced Study
Princeton, New Jersey
May 7 -10, 2018 - Number Theory Seminar
University of New South Wales Sydney
Sydney, Australia
March 13, 2018 - Pure Maths Seminar
University of New South Wales Sydney
Sydney, Australia
March 13, 2018 - Department Colloquium
University of New South Wales Canberra
Canberra, Australia
March 8, 2018 - Joint Mathematics Meetings
San Diego, CA
January 10 – 13, 2018
2017
- Department Colloquium
Oberlin College, Oberlin, OH
November 29, 2017 - Algebra, Geometry, and Number Theory Seminar
Tufts University, Boston, MA
November 16, 2017 - Mathematics & Statistics Department Colloquium
Elon University, Elon, NC
October 18, 2017 - WIN4
Banff International Research Station, Canada
August 14 – 18, 2017 - MCA 2017
Special Session Advances in algebraic and analytic number theory (co-organizer)
Montréal, Canada
July 24 – 28, 2017 - SWIM 2017 (course lecturer)
Duke University, Durham, NC
July 20 – 30, 2017 - Careers in Academia
AIM, San Jose, California
June 6 – 9, 2017 - re:boot number theory 2017 (co-organizer)
Duke University, Durham, NC
June 1 – 3, 2017 - AMS Spring Western Sectional Meeting
Special Session Analytic number theory and automorphic forms (invited speaker)
Washington State University
April 22 – 23, 2017 - Algebraic Geometry and Number Theory Seminar
Rice University
April 11, 2017 - MSRI Analytic Number Theory Semester Program
Connections for Women (invited speaker)
Program Member (postdoc)
MSRI, Berkeley, CA
January 17 – May 26, 2017 - Joint Mathematics Meetings
AMS Special Session Analytic number theory and arithmetic (invited speaker)
MAA Invited Paper Session L-functions and other animals (co-organizer)
Atlanta, Georgia
January 4 – 7, 2016
2016
- Number Theory Seminar
University of South Carolina
November 17, 2016 - Harkness Table Series
Spartanburg Day School
October 21, 2016 - Moments of zeta and correlations of divisor sums
AIM, San Jose, California
August 29 – September 2, 2016 - WADE Into Research (invited speaker)
Wake Forest University, Winston-Salem, NC
June 24, 2016 - SWIM (invited speaker)
Duke University, Durham, NC
June 21, 2016 - Winthrop University REU (invited speaker)
Winthrop University, Rock Hill, SC
June 17, 2016 - Number Theory Seminar
University of Illinois Urbana-Champaign
April 21, 2016 - Department Colloquium
Wake Forest University, Winston-Salem, NC
April 6, 2016 - Department Colloquium
Winthrop University, Rock Hill, SC
April 1, 2016 - re:boot Number Theory 2016 (co-organizer)
Duke University, Durham, NC
March 17-20, 2016 - 30th Automorphic Forms Workshop
Wake Forest University, Winston-Salem, NC
March 7-10, 2016
2015
- Computational Aspects of the Langlands Program (invited speaker)
ICERM, Providence, Rhode Island
November 8-21, 2015 - Elementary, analytic, and algorithmic number theory: Research inspired by the mathematics of Carl Pomerance (invited speaker)
University of Georgia, Athens, GA
June 9-11, 2015 - Analytic Methods in Elementary Number Theory (invited speaker)
AMS Special Session Southeastern Sectional
University of Alabama, Huntsville, AL
March 27-29, 2015 - Department Colloquium
Williams College, Williamstown, MA
January 23, 2015 - UNC-Duke Number Theory Seminar
Duke University, Durham, NC
January 21, 2015 - 2015 Joint Mathematics Meetings
San Antonio, TX
January 10-13, 2015
2014
- New Approaches in Probabilistic and Multiplicative Number Theory
CRM, Montréal, Canada
December 8-12, 2014 - Bounded Gaps Between Primes
AIM, Palo Alto, CA
November 17-21, 2014 - Young Mathematicians Conference
Ohio State University, Columbus, Ohio
August 22-24, 2014 - ENFANT & ELEFANT
Hausdorff Center, Bonn, Germany
July 11-18, 2014
Preprints
- Short mollifiers of the Riemann zeta-function (with J.B. Conrey, D.W. Farmer, C.-H. Kwan, and Y. Lin), 2025 [preprint]
- The Alternative Hypothesis for zeros of the Riemann zeta-function (with S. Baluyot, D.A. Goldston, and A.I. Suriajaya), 2025 [preprint]
- A guide to Tauberian theorems for arithmetic applications (with L. Pierce and A. Zaman), 2025 [preprint]
- Pair correlation of zeros of the Riemann zeta function I: Proportions of simple zeros and critical zeros (with S. Baluyot, D.A. Goldston, and A.I. Suriajaya), 2025 [preprint]
Publications
- A mean value theorem for Dirichlet polynomials associated with primitive Dirichlet L-functions, with S. Baluyot, International Mathematics Research Notices, 2025(3) (2025), 1-39 [accepted manuscript] [journal]
- This article is the streamlined version of a longer preprint: Twisted 2k-th moments of primitive Dirichlet L-functions: beyond the diagonal, with S. Baluyot, [preprint]
- An unconditional Montgomery Theorem for pair correlation of zeros of the Riemann zeta function, with S. Baluyot, D.A. Goldston, and A. I. Suriajaya, Acta Arithmetica 214 (2024), 357-376 [preprint] [journal]
- On the Montgomery-Odlyzko method regarding gaps between zeros of the zeta-function, with D. A. Goldston and T. S. Trudgian, in press, Journal of Mathematical Analysis and Applications, 2023 [preprint] [journal]
- Some explicit and unconditional results on gaps between zeroes of the Riemann zeta-function, with T. Trudgian and A. Simonič, Transactions of the American Mathematical Society, 375, no. 3 (2022), 3239-3265. [preprint] [journal]
- Hilbert transforms and the equidistribution of zeros of polynomials, with E. Carneiro, M. K. Das, A. Florea, A. V. Kumchev, A. Malik, M. B. Milinovich, and J. Wang, Journal of Functional Analysis, 281 (2021), no. 9, Paper No. 109199, 25 pp. [preprint] [journal]
- On a conjecture for l-torsion in class groups of number fields: from the perspective of moments, with L. B. Pierce and M. Matchett Wood, Mathematical Research Letters, 28, no. 2 (2021), pp. 575-621. [preprint] [journal]
- An effective Chebotarev density theorem for families of number fields with an application to l-torsion in class groups, with L. B. Pierce and M. Matchett Wood, Inventiones Mathematicae, 219 (2020), no. 2, 701-778. [preprint] [journal]
- Extremal primes of elliptic curves without complex multiplication, with C. David, A. Gafni, A. Malik, and N. Prabhu, Proceedings of the American Mathematical Society, 148 (2020), no. 3, 929-943. [preprint] [journal]
- On r-gaps between zeros of the Riemann zeta-function, with J. B. Conrey, Bulletin of the London Mathematical Society, 50 (2018) no. 2, 349-356. [preprint] [journal]
- Gaps between zeros of Dedekind zeta-functions of quadratic number fields. II, with H.M. Bui and W.P. Heap, Quarterly Journal of Mathematics, 67 (2016) no. 3, 467-482. [preprint] [journal]
- Gaussian distribution of the number of summands in generalized Zeckendorf decompositions in small intervals, with A. Best, P. Dynes, X. Edelsbrunner, B. McDonald, S. J. Miller, K. Tor, and M. Weinstein, INTEGERS, 16 (2016), #A6. [preprint] [journal] (collaboration with undergraduates at the 2014 SMALL REU)
- Gaussian behavior of the number of summands in Zeckendorf decompositions in small intervals, with A. Best, P. Dynes, X. Edelsbrunner, B. McDonald, S. J. Miller, K. Tor, and M. Weinstein, Fibonacci Quarterly, 52 (2014), no. 5, 35-46. [preprint] [article]
- Benford behavior of Zeckendorf decompositions, with A. Best, P. Dynes, X. Edelsbrunner, B. McDonald, S. J. Miller, K. Tor, and M. Weinstein, Fibonacci Quarterly, 52 (2014), no. 5, 47-53. [preprint] [article]
- Consecutive primes in tuples, with W. D. Banks and T. M. Freiberg, Acta Arithmetica, 167 (2015), 261-266. [preprint] [journal]
- Gaps between zeros of GL(2) L-functions, with O. Barrett, B. McDonald, S. J. Miller, P. Ryan, and K. Winsor, Journal of Mathematical Analysis and Applications, 429 (2015), 204-232. [preprint] [journal] (collaboration with undergraduates at the 2014 SMALL REU)
- Gaps between zeros of Dedekind zeta-functions of quadratic number fields, Journal of Mathematical Analysis and Applications, 418 (2014), no. 1, 100-107. [journal]
- Moments of products of automorphic L-functions, with M. B. Milinovich, Journal of Number Theory, 139 (2014), 175-204. [journal]
Conference Proceedings (with undergraduates at the SMALL 2014 REU)
- Benford behavior of generalized Zeckendorf decompositions, with A. Best*, P. Dynes, X. Edelsbrunner, B. McDonald, S. J. Miller, and M. Weinstein, Combinatorial and Additive Number Theory II: CANT, New York, NY, USA, 2015 and 2016, Springer, New York, 2017. [preprint] [article]
Book Contributions (with undergraduates at the SMALL 2014 REU)
- From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond, with O. Barrett, F. W. K. Firk, and S. J. Miller, Chapter in Open Problems in Mathematics (editors John Nash Jr. and Michael Th. Rassias), Springer-Verlag (2016). [preprint] [chapter]
- Some Results in the Theory of Low-lying Zeros, with B. Mackall, S. J. Miller, C. Rapti, and K. Winsor, in Families of automorphic forms and the trace formula (editors Werner Müller, Sug Woo Shin, and Nicolas Templier), Simons Symposia Series, Springer-Verlag. [preprint] [chapter]
- Benfordness of the Cauchy Distribution and Generalizations, with X. Edelsbrunner, K. Huan, B. Mackall, J. Powell, and M. Weinstein, Section 3.6, an appendix to Benford’s Law: Theory and Applications, (S. J. Miller, editor), Princeton University Press, 2015. [chapter]
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