Dr. Jeremy Rouse

Associate Professor, Sterge Faculty Fellow and Graduate Program Coordinator

Dr. Rouse’s

Contact Information

Office: Manchester 128
Phone: (336) 758-4159
Home Page: http://www.wfu.edu/~rouseja/
Email: rouseja 'at' wfu.edu

Degrees

Ph.D., Mathematics, 2007, University of Wisconsin
M.A., Mathematics, 2005, University of Wisconsin
B.S., Mathematics, 2003, Harvey Mudd College

Research Interests

Modular and Automorphic Forms.
L-functions.
Elliptic Curves and Abelian Varieties.
Quadratic Forms.

Publications

Professional Website

Recent publications For online access to published versions of the articles below, see this page.

A. Bourdon, D. Gill, J. Rouse, L. Watson, 'Odd degree isolated points on X₁(N) with rational j-invariant', preprint. (Code is available here.)
M. Cerchia, J. Rouse, 'Uniform bounds on the image of the arboreal Galois representation attached to non-CM elliptic curves', accepted for publication in Proceedings of the American Mathematical Society.
J. Holley-Reid, J. Rouse, 'The number of representations of n as a growing number of squares', submitted.
C. Donnay, S. R. Garcia, J. Rouse, 'p-adic quotient sets II: quadratic forms', Journal of Number Theory 201 (2019), 23-39.
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, 1547-1563.
J. Rouse, 'Integers represented by positive-definite quadratic forms and Petersson inner products', Acta Arithmetica 187 (2019) no. 1, 81-100.
S. Binegar, R. Dominick, M. Kenney, J. Rouse, A. Walsh, 'An Elliptic Curve Analogue to the Fermat Numbers', Involve 12 (2019), no. 3, 427-449.
J. DeBenedetto, J. Rouse, 'Quadratic forms representing all integers coprime to 3', Ramanujan Journal 46 (2016), no. 2, 431-446.
G. Dresden, K. Hess, S. Islam, J. Rouse, A. Schmitt, E. Stamm, T. Warren, P. Yue, 'When is aⁿ + 1 the sum of two squares?', Involve 12 (2019), no. 4, 585-605.
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, 1881-1894.
A. Block Gorman, T. Genao, H. Hwang, N. Kantor, S. Parsons, J. Rouse, 'The density of primes dividing a particular non-linear recurrence sequence,' Acta Arithmetica 175 (2016) no. 1, 71-100.
B. Davis, R. Kotsonis, J. Rouse, 'The density of primes dividing a term in the Somos-5 sequence,' Proceedings of the American Mathematical Society, Series B 4 (2017), 5-20.
J. Rouse, Y. Yang, 'Three consecutive almost squares,' International Journal of Number Theory 12 (2016), no. 4, 969-978.
J. Rouse, D. Zureick-Brown, 'Elliptic curves over Q and 2-adic images of Galois,' Research in Number Theory, 1 (2015).
J. Rouse, J. J. Webb, 'Spaces of modular forms spanned by eta-quotients,' Advances in Mathematics, 272 (2015), 200-224.
J. Rouse, J. Thorner, 'The explicit Sato-Tate conjecture and densities pertaining to Lehmer-type questions,' Transactions of the American Mathematical Society 369 (2017) no. 5, 3575-3604.
P. Cubre, J. Rouse, 'Divisibility properties of the Fibonacci entry point,' Proceedings of the American Mathematical Society, 142 (2014), no. 11, 3771-3785.
M. Jones, J. Rouse, 'Solutions of the cubic Fermat equation in quadratic fields,' International Journal of Number Theory, 9 (2013), no. 6, 1579-1591.
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, 243-256.
J. Rouse, 'Quadratic forms representing all odd positive integers,' American Journal of Mathematics, 136 (2014), no. 6, 1693-1745.
J. Rouse, 'Explicit bounds for sums of squares,' Mathematical Research Letters, 19 (2012), no. 2, 359-376.
P. Jenkins, J. Rouse, 'Bounds for coefficients of cusp forms and extremal lattices,' Bulletin of the London Mathematical Society, 43 (2011), no. 5, 927-938.
B. Reznick, J. Rouse, 'On the sums of two cubes,' International Journal of Number Theory, 7 (2011), no. 7, 1863-1882.

Curriculum vitae

Classes

Instructor, MST 321, Spring 2020.
Instructor, MST 117, Spring 2020.
Instructor, MST 121 sections A and B, Fall 2019.
Instructor, MST 165, Fall 2019.
Instructor, MST 321, Spring 2019.
Instructor, MST 121 sections A and B, Spring 2019
Instructor, MST 321, Fall 2018.
Instructor, MST 243, Fall 2018.
Instructor, MST 165, Fall 2018.
Instructor, MST 121 sections B and C, Spring 2018.
Instructor, MST 346/646, Fall 2017.
Instructor, MST 121, Fall 2017.
Instructor, MST 165, Fall 2017.
Instructor, MTH 345/645, Spring 2017.
Instructor, MTH 121, Spring 2017.
Instructor, MTH 345/645, Spring 2016.
Instructor, MTH 112 sections C and D, Spring 2016.
Instructor, MTH 113 section C, Fall 2015.
Instructor, MTH 165, Fall 2015.
Instructor, MTH 346/646, Fall 2015.
Instructor, MTH 121 sections A and B, Spring 2015.
Instructor, MTH 113 section B, Fall 2014.
Instructor, MTH 243, Fall 2014.
Instructor, MTH 165, Fall 2014.
Instructor, MTH 345/645, Spring 2014.
Instructor, MTH 111 section E, Spring 2014.
Instructor, MTH 111 section J, Fall 2013.
Instructor, MTH 117 section A, Fall 2013.
Instructor, MTH 165, Fall 2013.
Instructor, MTH 345/645, Spring 2013.
Instructor, MTH 113 section A, Spring 2013.
Instructor, MTH 745, Spring 2012.
Instructor, MTH 722, Spring 2012.
Instructor, MTH 113 section B, Spring 2012.
Instructor, MTH 165, Fall 2011.
Instructor, MTH 721, Fall 2011.
Instructor, MTH 346/646, Fall 2011.
Instructor, MTH 113 section A, Spring 2011.
Instructor, MTH 345/645, Spring 2011.
Co-Instructor (with Jason Parsley), MTH 165 section B, Fall 2010.
Instructor, MTH 112 sections B and C, Fall 2010.

Awards

A.J. Sterge Faculty Fellow, 2020-2023.
National Security Agency Grant for the 2016 Automorphic Forms Workshop, $14,400.
National Science Foundation Grant, 2015-2018, DMS-1461189, REU Site: Wake/Davidson Experience In Number Theory Research (PI, with co-PI Katherine Thompson), $258,354.
2014 TLC Teaching Innovation Award.
CRADLE IV Fellow, 2013-2015.
A.J. Sterge Faculty Fellow, 2013-2016.
List of Teachers Ranked as Excellent By Their Students, Spring 2010, Math 453.
National Science Foundation Grant, 2009-2012, DMS-0901090, The distribution of Fourier coefficients of modular forms and arithmetic applications (PI), $83,651.
Project NExT Fellow, 2008-2009.
University Housing's Favorite Instructor Award, Spring 2007.
NDSEG Fellowship, sponsored by the Department of Defense and the Office of Naval Research, 2003-2006.
Honorable mention in the 2002 William Lowell Putnam Mathematical Competition.

Personal Interests

Chess and Choral Singing