BYU Computational Number Theory Research Group

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Dr. Paul Jenkins, Department of Mathematics

The computational number theory group has clearly been a success, with students writing papers, giving conference presentations, winning prestigious national fellowships, and going off to strong PhD programs in mathematics. The weekly seminar has helped students learn presentation skills and learn more mathematics, and has provided a convenient entry point for new students interested in research. It is anticipated that the group will continue into the foreseeable future, and that students will continue to benefit from the allocated resources.

In 2011–2012, the following students participated in undergraduate research with the four faculty members involved in this MEG. Papers, talks, etc. are noted for each student.

  • Michael Griffin, fall 2009–winter 2011, Paul Jenkins and Darrin Doud
    • M. Griffin, Divisibility properties of coefficients of weight 0 weakly holomorphic modular forms, International Journal of Number Theory 7 (2011), no. 4, 933–941
    • National Physical Science Consortium Fellowship
    • 2011 NSF Graduate Research Fellowship
    • Attended The Number Theory of Partitions conference, Emory University, January 2011
    • Spoke at 2011 Automorphic Forms Workshop, Oregon State University
    • Spoke at 2011 CPMS Student Research Conference
  • Nick Andersen, summer 2010–spring 2011, Paul Jenkins and Darrin Doud
    • N. Andersen and P. Jenkins, 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]
    • 2011 NSF Graduate Research Fellowship Honorable Mention
    • Spoke at 2011 Automorphic Forms Workshop, Oregon State University
    • Attended The Number Theory of Partitions conference, Emory University, January 2011
    • Spoke at 2011 CPMS Student Research Conference
  • Adele Lopez, winter 2010–summer 2012, Paul Jenkins and Darrin Doud
    • D. Doud, P. Jenkins and J. Lopez, Two-divisibility of the coefficients of certain weakly holomorphic modular forms, The Ramanujan Journal 28 (2012), no. 1, 89–111, doi: 10.1007/s11139-011-9331-0, arXiv:1105.0684v2 [math.NT]
    • 2012 NSF Graduate Research Fellowship
    • Attended The Number Theory of Partitions conference, Emory University, January 2011
    • Spoke at 2011 Automorphic Forms Workshop, Oregon State University
    • Attended REU at Mt. Holyoke, summer 2011
    • Spoke at 2011, 2012 CPMS Student Research Conference
    • Attended 2012 American Mathematical Society sectional meeting and number theory conference, University of Hawaii
  • Jocelyn Peck, winter 2010–winter 2011, Paul Jenkins and Darrin Doud
    • Spoke at 2011 CPMS Student Research Conference
    • Attended 2011 Nebraska Conference for Undergraduate Women in Mathematics
    • Attended The Number Theory of Partitions conference, Emory University, January 2011
    • Attended 2011 Automorphic Forms Workshop, Oregon State University
  • Chris Hettinger, winter 2011–present, Paul Jenkins and Darrin Doud
    • Spoke at 2011, 2012 CPMS Student Research Conference
    • Funded by MEG to mentor Kyle Pratt, Andrew Haddock, DJ Thornton in modular forms research, summer 2012
    • Attended 2012 American Mathematical Society sectional meeting and number theory conference, University of Hawaii
  • Mason Victors, fall 2010–summer 2011, Paul Jenkins
    • C. Guzman, B. Tuckfield, and M. Victors, Patterns in orders of elliptic curves over finite fields, submitted for publication
    • Spoke at 2011 CPMS Student Research Conference
  • Bradford Tuckfield, fall 2010–summer 2011, Paul Jenkins
    • C. Guzman, B. Tuckfield, and M. Victors, Patterns in orders of elliptic curves over finite fields, submitted for publication
    • Spoke at 2011 CPMS Student Research Conference
  • Chris Guzman, fall 2010–summer 2011, Paul Jenkins
    • C. Guzman, B. Tuckfield, and M. Victors, Patterns in orders of elliptic curves over finite fields, submitted for publication
    • Spoke at 2011 CPMS Student Research Conference
  • Kyle Pratt, spring 2012-present, Paul Jenkins
    • P. Jenkins and K. Pratt, Interlacing of zeros of weakly holomorphic modular forms, in preparation
  • Andrew Haddock, spring 2012-present, Paul Jenkins
    • A. Haddock and P. Jenkins, Zeros of weakly holomorphic modular forms of level 4, in preparation
  • DJ Thornton, spring 2012-present, Paul Jenkins
    • P. Jenkins and D. Thornton, Congruences for coefficients of weakly holomorphic modular forms of level 4, in preparation
  • Nathan Green, fall 2010–present, David Cardon and Paul Jenkins
    • N. Green and P. Jenkins, Integrality properties for traces of singular moduli of prime level, in preparation
    • Attended 1st EU-US Conference on Automorphic Forms and Related Topics, RWTH Aachen University, Germany, 2012
    • Spoke at Palmetto Number Theory Series conference, University of South Carolina, fall 2012
    • Spoke at 2011, 2012 CPMS Student Research Conference
    • Research assistantship funded by MEG, winter 2012
  • Samuel Dittmer, 2011–present, Pace Nielsen
    • Spoke at 2012 American Mathematical Society sectional meeting and number theory conference, University of Hawaii
    • S. Dittmer, Spoof odd perfect numbers, Mathematics of Computation, to appear
    • S. Dittmer, D. Khurana, P. Nielsen, On a question of Hartwig and Luh, in preparation
    • Spoke at 2012 CPMS Student Research Conference
  • S. Adam Fletcher, 2011, Pace Nielsen
    • S. A. Fletcher, P. Nielsen, P. Ochem, Sieve methods for odd perfect numbers, Math. Comp. 81 (2012), 1753–1776.
    • Spoke at 2011 CPMS Student Research Conference
  • Derek McDaniel, 2011, Pace Nielsen
    • Spoke at 2011 CPMS Student Research Conference
    • Wrote program available at http://trqrt.com/projects/unitcolorplane/index
  • Vinh Dang, 2010–2011, Darrin Doud
    • Spoke at 2011 CPMS Student Research Conference
    • 2011 master’s thesis
  • Ka Lun Wong, 2010–2011, Darrin Doud
    • Spoke at 2011 CPMS Student Research Conference
    • 2011 master’s thesis
  • Joe Keller, 2011–2012, Darrin Doud
    • Spoke at 2012 CPMS Student Research Conference • Becky Brogan, winter 2011, David Cardon
    • Spoke at 2011 CPMS Student Research Conference

The main items for which the MEG budget was spent include the following:

  • One semester of research assistantship for Nathan Green as he began the BYU MS Mathe- matics program.
  • One summer of research assistantship for Chris Hettinger; he provided mentoring to three new research students, quickly bringing them up to speed on the topics they are studying.
  • Travel for four students to attend the Number Theory of Partitions conference at Emory University in January 2011.
  • Travel for four students to attend (and three to speak at) the 2011 Automorphic Forms Workshop at Oregon State University.
  • Travel for three students to attend (one to speak at) the 2012 AMS Sectional Meeting and subsequent number theory conference at the University of Hawaii.
  • Travel for Nathan Green to attend the two week summer school and conference on auto- morphic forms in Aachen, Germany, in summer 2012.
  • Travel for three students to attend and speak at the 2013 Automorphic Forms Workshop in Dublin, Ireland.