Jeremy Rouse Professor and Graduate Program Coordinator Department of Mathematics Wake Forest University P.O. Box 7388 Winston-Salem, NC 27109 (336) 758-4159 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 x³ + x² y² + y³ = k', submitted.
• J. Rouse, A. Sutherland, D. Zureick-Brown, 'l-adic 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, 166-177. (Code is available here.)
• A. Bourdon, D. Gill, J. Rouse, L. Watson, 'Odd degree isolated points on X₁(N) with rational j-invariant', submitted. (Code is available here.)
• M. Cerchia, J. Rouse, 'Uniform bounds on the image of the arboreal Galois representation attached to non-CM elliptic curves', Proceedings of the American Mathematical Society 149 (2021), no. 2, 583-589.
• J. Holley-Reid, 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, '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.

Research Interests

• Modular and Automorphic Forms.
• L-functions.
• 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, 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.

Curriculum Vitae

Links

• Wake Forest University Number Theory Seminar.
• If you want a letter of recommendation from me, please see this page.
• Material from the University of Georgia CAAATQuafs conference.
• The Wake Forest University Department of Mathematics.
• The University of Illinois, Urbana-Champaign Math Department
• The University of Wisconsin-Madison Math Department
• Harvey Mudd College Math Department
• Budapest Semesters in Mathematics Program
• Interesting Math Problems I've Seen
• A random amusement
• Cat pictures
• A wide variety of links to mathematical stuff on the web.

Last modified: Friday, 25-Aug-2023 14:30:05 EDT