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