# Caroline Turnage-Butterbaugh

### Research Areas and Keywords

##### Number Theory

### Selected Grants

Re:boot Number Theory awarded by National Security Agency (Co-Principal Investigator). 2016 to 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)

Mackall, B, Miller, SJ, Rapti, C, Turnage-Butterbaugh, C, and Winsor, K. "Some Results in the Theory of Low-lying Zeros." *Families of Automorphic Forms and the Trace Formula.* Springer, September 20, 2016. (Chapter)

Barrett, O, Firk, F, Miller, SJ, and Turnage-Butterbaugh, C. "From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond." *Open Problems in Mathematics.* Springer, August 6, 2016. 123-171. (Chapter)

Edelsbrunner, X, Huan, K, Mackall, B, Powell, J, Turnage-Butterbaugh, C, and Weinstein, M. "Benfordness of the Cauchy Distribution and Generalizations." *Benford's Law Theory and Applications.* Princeton University Press, June 9, 2015. (Appendix)

Pierce, LB, Turnage-Butterbaugh, 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).
Open Access Copy

Best, A, Dynes, P, Edelsbrunner, X, McDonald, B, Miller, SJ, Tor, K, Turnage-Butterbaugh, C, and Weinstein, M. "Benford Behavior of Generalized Zeckendorf Decompositions." *Springer Proceedings in Mathematics and Statistics* 220 (January 1, 2017): 25-37.
Full Text

Bui, HM, Heap, WP, and Turnage-Butterbaugh, CL. "GAPS BETWEEN ZEROS OF DEDEKIND ZETA-FUNCTIONS OF QUADRATIC NUMBER FIELDS. II." *The Quarterly Journal of Mathematics* 67.3 (September 1, 2016): 467-482.
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Best, A, Dynes, P, Edelsbrunner, X, McDonald, B, Miller, SJ, Tor, K, Turnage-Butterbaugh, 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, Turnage-Butterbaugh, CL, and Winsor, K. "Gaps between zeros of GL(2) L-functions." *Journal of Mathematical Analysis and Applications* 429.1 (September 2015): 204-232.
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Banks, WD, Freiberg, T, and Turnage-Butterbaugh, CL. "Consecutive primes in tuples." *Acta Arithmetica* 167.3 (2015): 261-266.
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Turnage-Butterbaugh, CL. "Gaps between zeros of Dedekind zeta-functions of quadratic number fields." *Journal of Mathematical Analysis and Applications* 418.1 (October 2014): 100-107.
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Milinovich, MB, and Turnage-Butterbaugh, CL. "Moments of products of automorphic L-functions." *Journal of Number Theory* 139 (June 2014): 175-204.
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Best, A, Dynes, P, Edelsbrunner, X, McDonald, B, Miller, SJ, Tor, K, Turnage-Butterbaugh, C, and Weinstein, M. "Benford behavior of Zeckendorf decompositions." *Fibonacci Quarterly* 52.5 (2014): 35-46.

Best, A, Dynes, P, Edelsbrunner, X, McDonald, B, Miller, SJ, Tor, K, Weinstein, M, and Turnage-Butterbaugh, C. "Gaussian behavior of the number of summands in Zeckendorf decompositions in small intervals." *Fibonacci Quarterly* 52.5 (2014): 47-53.