Jeremy Rouse
Professor and Graduate Program Coordinator
Department of Mathematics
Wake Forest University
P.O. Box 7388
WinstonSalem, NC 27109
(336) 7584159
rouseja 'at' wfu dot edu


Recent publications
For online access to published versions of the articles below,
see this
page.
 P. Clark, P. Pollack, J. Rouse, K. Thompson, 'Densities of sets of integers represented by quadratic forms', submitted.
 J. Rouse, K. Thompson, 'Quaternary quadratic forms with prime discriminant', accepted for publication in Acta Arithmetica.
 X. Lang, J. Rouse, 'Rational points on x^{3} + x^{2} y^{2} + y^{3} = k', submitted.
 J. Rouse, A. Sutherland, D. ZureickBrown, 'ladic images of Galois for elliptic curves over Q, Forum of Mathematics, Sigma 10, (2022), Paper No. e62. (Code is available here.)
 A. Newton, J. Rouse, 'Integers that are sums of two rational sixth powers, Canadian Mathematical Bulletin 66 (2023), no. 1, 166177. (Code is available here.)
 A. Bourdon, D. Gill, J. Rouse, L. Watson, 'Odd degree isolated points on X_{1}(N)
with rational jinvariant', submitted. (Code is available here.)
 M. Cerchia, J. Rouse, 'Uniform bounds on the image of the arboreal Galois representation attached to nonCM elliptic curves', Proceedings of the American Mathematical Society
149 (2021), no. 2, 583589.
 J. HolleyReid, J. Rouse, 'The number of representations of n as a growing number of squares', accepted for publication in Involve.
 C. Donnay, S. R. Garcia, J. Rouse, 'padic quotient sets II: quadratic forms', Journal of Number Theory 201 (2019), 2339.
 K. Liang, J. Rouse, 'The density of odd order reductions for elliptic curves with a rational point of order 2', International Journal of Number Theory 15 (2019), no. 8, 15471563.
 J. Rouse, 'Integers represented by positivedefinite quadratic forms and Petersson inner products', Acta Arithmetica 187 (2019) no. 1, 81100.
 S. Binegar, R. Dominick, M. Kenney, J. Rouse, A. Walsh, 'An Elliptic Curve Analogue to the Fermat Numbers', Involve 12 (2019), no. 3, 427449.
 J. DeBenedetto, J. Rouse, 'Quadratic forms representing all integers coprime to 3', Ramanujan Journal 46 (2016), no. 2, 431446.
 G. Dresden, K. Hess, S. Islam, J. Rouse, A. Schmitt, E. Stamm, T. Warren, P. Yue, 'When is a^{n} + 1 the sum of two squares?', Involve 12 (2019), no. 4, 585605.
 B. Goddard, J. Rouse, 'Sum of two repdigits a square,' Integers 17 (2017), Paper No. A24.
 J. Patsolic, J. Rouse, 'Trinomials defining quintic number fields,' International Journal of Number Theory 13 (2017), no. 7, 18811894.
 A. Block Gorman, T. Genao, H. Hwang, N. Kantor, S. Parsons, J. Rouse,
'The density of primes dividing a particular nonlinear recurrence sequence,' Acta Arithmetica 175 (2016) no. 1, 71100.
 B. Davis, R. Kotsonis, J. Rouse, 'The density of primes dividing a term in the Somos5 sequence,' Proceedings of the American Mathematical Society, Series B 4 (2017), 520.
 J. Rouse, Y. Yang, 'Three consecutive almost squares,' International Journal of Number Theory 12 (2016), no. 4, 969978.
 J. Rouse, D. ZureickBrown, 'Elliptic curves over Q and 2adic images of Galois,' Research in Number Theory, 1 (2015).
 J. Rouse, J. J. Webb, 'Spaces of modular forms spanned by etaquotients,' Advances in Mathematics, 272 (2015), 200224.
 J. Rouse, J. Thorner, 'The explicit SatoTate conjecture and densities pertaining to Lehmertype questions,' Transactions of the American Mathematical Society 369 (2017) no. 5, 35753604.
 P. Cubre, J. Rouse, 'Divisibility properties of the Fibonacci entry point,' Proceedings of the American Mathematical Society, 142 (2014), no. 11, 37713785.
 M. Jones, J. Rouse, 'Solutions of the cubic Fermat equation in quadratic fields,' International Journal of Number Theory, 9 (2013), no. 6, 15791591.
 J. Rouse, F. Thorne, 'On the existence of large degree Galois representations for fields of small discriminant,' Pacific Journal of Mathematics, 271 (2014), no. 1, 243256.
 J. Rouse, 'Quadratic forms representing all odd positive integers,' American Journal of Mathematics, 136 (2014), no. 6, 16931745.
 J. Rouse, 'Explicit bounds for sums of squares,' Mathematical Research Letters, 19 (2012), no. 2, 359376.
 P. Jenkins, J. Rouse, 'Bounds for
coefficients of cusp forms and extremal lattices,' Bulletin of the London Mathematical Society, 43 (2011), no. 5, 927938.
 B. Reznick, J. Rouse, 'On the sums of two cubes,' International Journal of Number Theory, 7 (2011), no. 7, 18631882.
Research Interests
 Modular and Automorphic Forms.
 Lfunctions.
 Elliptic Curves and Abelian Varieties.
 Quadratic Forms.
Teaching
 Instructor, MTH 113, MTH 165, and MTH 721, Fall 2023.
 Instructor, MTH 345/645 (joint with Abbey Bourdon), Summer 2023.
 Instructor, MTH 311 and MTH 165, Spring 2023.
 Instructor, MST 311, Spring 2022.
 Instructor, MST 121 and MST 165, Fall 2021.
 Instructor, MST 112, Summer 2021.
 Instructor, MST 113, MST 345/645, Spring 2021.
 Instructor, MST 113, MST 165, Fall 2020.
 Instructor, MST 117, MST 321, Spring 2020.
 Instructor, MST 121 and MST 165, Fall 2019.
 Instructor, MST 121 and MST 321, Spring 2019.
 Instructor, MST 165, MST 243, and MST 321, Fall 2018.
 Instructor, MST 121, Spring 2018.
 Instructor, MST 121, MST 165, and MST 346/646, Fall 2017.
 Instructor, MTH 121 and MTH 345/645, Spring 2017.
 Instructor, MTH 112, MTH 345/645, Spring 2016.
 Instructor, MTH 113, MTH 165, and MTH 346/646, Fall 2015.
 Instructor, MTH 121, Spring 2015.
 Instructor, MTH 113, MTH 243, Fall 2014.
 Instructor, MTH 111, MTH 345/645, Spring 2014.
 Instructor, MTH 111, MTH 117, MTH 117, Fall 2013.
 Instructor, MTH 113, MTH 345/645, Spring 2013.
 Instructor, MTH 113, MTH 722, MTH 745, Spring 2012.
 Instructor, MTH 165, MTH 346/646, MTH 721, Fall 2011.
 Instructor, MTH 113, MTH 345/645, Spring 2011.
 Instructor, MTH 112, MTH 165 (joint with Jason Parsley), Fall 2010.
Awards
 A.J. Sterge Faculty Fellow, 20202023.
 National Security Agency Grant for the 2016 Automorphic Forms Workshop,
$14,400.
 National Science Foundation Grant, 20152018,
DMS1461189, REU Site: Wake/Davidson Experience In Number Theory Research (PI, with coPI Katherine Thompson), $258,354.
 2014 TLC Teaching Innovation Award.
 CRADLE IV Fellow, 20132015.
 A.J. Sterge Faculty Fellow, 20132016.
 List of Teachers Ranked as Excellent By Their Students,
Spring 2010, Math 453.
 National Science Foundation Grant, 20092012,
DMS0901090,
The distribution of Fourier coefficients of modular forms
and arithmetic applications (PI), $83,651.
 Project NExT
Fellow,
20082009.
 University Housing's Favorite Instructor Award, Spring 2007.
 NDSEG Fellowship, sponsored by the Department of Defense and
the
Office of Naval Research, 20032006.
 Honorable mention in the 2002 William Lowell Putnam
Mathematical
Competition.
Links
Last modified: Friday, 25Aug2023 14:30:05 EDT