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Physical and Mathematical Sciences
Math
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Paul Jenkins

Professor - Department Chair
Curriculum Vitae
Permanent Faculty
Website: https://math.byu.edu/~jenkins
Email: jenkins@math.byu.edu

Office: 279 TMCB

801-422-5868

Office Hours: MWF 2-2:50pm

Class Schedule: Math 682 Section 001 MWF 3-3:50pm 116 TMCB

Research Interests: Number theory, including modular forms, partitions, and odd perfect numbers.

Degrees: Brigham Young University, BS in Mathematics (2000), MS in Mathematics (2002), University of Wisconsin-Madison, PhD in Mathematics(2006)

Prizes and Awards:

  1. Robert Sorgenfrey Distinguished Teaching Award, UCLA Mathematics Department, 2008
  2. Distinguished Mentoring Award, BYU Department of Mathematics, 2011

Publications:

  1. M. Griffin, P. Jenkins, and G. Molnar, The arithmetic of modular grids, Mathematika 68 (2022), no. 4, 1080–1119, arXiv:2012.14403v3 [math.NT].
  2. BYU Computational Number Theory Group, Odd, spoof perfect factorizations, Journal of Number Theory 234 (2022), 31–47, arXiv:2006.10697v1 [math.NT].
  3. P. Jenkins and R. Keck, Congruences for coefficients of modular functions in levels 3, 5, and 7 with poles at 0, Journal of Number Theory 214 (2020), 13–26, doi:10.1016/j.jnt.2020.04.006, arXiv:2001.04337v2 [math.NT].
  4. K. Bringmann, P. Jenkins, and B. Kane, Differential operators on polar harmonic Maass forms and elliptic duality, Quarterly Journal of Mathematics 70 (2019), no. 4, 1181–1207, arXiv:1704.08649v1 [math.NT].
  5. V. Iba, P. Jenkins, and M. Warnick, Divisibility properties of coefficients of modular functions in genus zero levels, Integers 19 (2019), #A7, arXiv:1711.06239v2 [math.NT].
  6. P. Jenkins and G. Molnar, Zagier duality for level p weakly holomorphic modular forms, The Ramanujan Journal 50 (2019), no. 1, 93–109, doi: 10.1007/s11139-018-0009-8, arXiv:1709.10023v2 [math.NT].
  7. P. Jenkins, R. Keck, and E. Moss, Congruences for coefficients of level 2 modular functions with poles at 0, Archiv der Mathematik 111 (2018), no. 4, 369–378, doi: 10.1007/s00013-018-1207-8, arXiv:1709.10189v1 [math.NT].
  8. P. Jenkins and DJ Thornton, Weakly holomorphic modular forms in prime power levels of genus zero, Integers 18 (2018), #A18, arXiv:1703.08145v1 [math.NT].
  9. N. Green and P. Jenkins, Integral traces of weak Maass forms of genus zero odd prime level, The Ramanujan Journal 42 (2017), no. 2, 453–478, arXiv:1370.2204v1 [math.NT].
  10. A. Folsom and P. Jenkins, Zeros of modular forms of half integral weight, Research in Number Theory, 2:23 (2016), 1–25, http://link.springer.com/article/10.1007/s40993-016-0054-6.
  11. P. Jenkins and K. Pratt, Coefficient bounds for level 2 cusp forms and modular functions, Acta Arithmetica 168 (2015), 341–367, arXiv:1408.1083v1 [math.NT].
  12. P. Jenkins and DJ Thornton, Congruences for coefficients of modular functions, The Ramanujan Journal 38 (2015), no. 3, 619–628, arXiv:1404.0699v1 [math.NT].
  13. P. Jenkins and K. Pratt, Interlacing of zeros of weakly holomorphic modular forms, Proceedings of the American Mathematical Society, Series B 1 (2014), 63–77, arXiv:1308.1123v1 [math.NT].
  14. A. Haddock and P. Jenkins, Zeros of weakly holomorphic modular forms of level 4, International Journal of Number Theory 10, no. 2 (2014), 455–470, doi: 10.1142/S1793042113501030, arXiv:1305.3896v1 [math.NT].
  15. (with J. Rouse) Bounds for coefficients of cusp forms and extremal lattices, Bull. London Math. Soc., 43(5) (2011), 927-938.
  16. Odd perfect numbers have a prime factor exceeding 10^7, Mathematics of Computation 72 (2003), no. 243, 1549-1554.
  17. p-adic properties for traces of singular moduli, International Journal of Number Theory 1 (2005), no. 1, 103-107.
  18. (with J. Bruinier and K. Ono) Hilbert class polynomials and traces of singular moduli, Mathematische Annalen 334 (2006), no. 2, 373-393.
  19. Kloosterman sums and traces of singular moduli, Journal of Number Theory 117 (2006), no. 2, 301-314.
  20. (with K. Ono) Divisibility criteria for class numbers of imaginary quadratic fields, Acta Arithmetica 125 (2006), no. 3, 285-289.
  21. (with W. Duke) On the zeros and coefficients of certain weakly holomorphic modular forms, Pure and Applied Mathematics Quarterly 4 (2008), no. 4, 1327-1340.
  22. (with W. Duke) Integral traces of singular values of weak Maass forms, Algebra and Number Theory 2 (2008), no. 5, 573-593.
  23. (with D. Doud) p-adic properties of coefficients of weakly holomorphic modular forms, International Mathematics Research Notices, (16) (2010), 3184-3206.
  24. (with D. Doud and J. Lopez) Two-divisibility of the coefficients of certain weakly holomorphic modular forms, Ramanujan Journal 28 (2012), no. 1, 89-111, doi: 10.1007/s11139-011-9331-0, arXiv:1105.0684v2 [math.NT].
  25. (with N. Andersen) Divisibility properties of coefficients of level p modular functions for genus zero primes, Proceedings of the American Mathematical Society 141 (2013), 41-53, arXiv:1106.1188v1 [math.NT].
  26. (with S. Garthwaite) Zeros of weakly holomorphic modular forms of levels 2 and 3, submitted for publication, arXiv:1205.7050v1 [math.NT].