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Department of Mathematics

Number Theory Group


  • Todd Cochrane
    • Publications
    • Research Interests: Analytic Number Theory, Distribution of Solutions of Congruences and of Points on Varieties, Exponential Sums, Waring's Problem, Quadratic Forms, Trigonometric Sums, Additive Combinatorics

  • Craig Spencer
    • Publications
    • Research Interests: Analytic Number Theory, Arithmetic Geometry, Arithmetic Combinatorics, Hardy-Littlewood Circle Method, Diophantine Equations and Inequalities, Exponential Sums, Compressed Sensing, Discrepancy Theory

Emeritus Faculty

Faculty in Related Areas


Former Visitors and Postdoctoral Fellows

  • Sanying Shi, Visiting Professor (Hefei University of Technology), 2016-2017
  • Derrick Hart, Postdoctoral Fellow, 2011-2013
  • Jennifer Paulhus, Postdoctoral Fellow, 2007-2010
  • Sanying Shi, Visiting Graduate Student (Tongji University, Shanghai), 2009
  • John Garza, Postdoctoral Fellow, 2008-2009
  • Dominic Lanphier, Postdoctoral Fellow
  • Jason Rosenhouse, Postdoctoral Fellow
  • Kiryl Tishchanka, Postdoctoral Fellow
  • Kunrui Yu, Postdoctoral Fellow
  • Jungseob Lee, Postdoctoral Fellow
  • Zhiyong Zheng, Visiting Professor (Tsinghua University, Beijing)

Former Ph.D. Students

  • C. J. Richardson (Pinner), 2018, A generalization of the Goresky-Klapper conjecture
  • Misty Long (Cochrane and Spencer), 2016, Solutions of diagonal congruences with variables restricted to a box, First Position: Tenure-Track Assistant Professor at the University of Southern Indiana
  • Badria Alsulmi (Pinner), 2016, Generalized Jacobi sums modulo prime powers, First Position: Umm al-Quara University
  • Vincent Pigno (Pinner), 2014, Prime power exponential and character sums with explicit evaluations, First Position: Tenure-Track Assistant Professor at California State University, Sacramento
  • Dilum DeSilva (Cochrane and Pinner), 2013, Lind-Lehmer constant for groups of the form Zpn, First Position: Tenure-Track Assistant Professor at Bowling Green State University, Firelands College
  • James Cipra (Cochrane), 2010, Waring's problem over finite fields
  • Ishak Mohamed Ismail (Pinner), 2009, Lower bounds for heights in cyclotomic extensions and related problems
  • Ala' Jamil Alnaser (Cochrane), 2009, Waring's problem in algebraic number fields
  • Ali Hakami (Cochrane), 2009, Small zeros of quadratic congruences to a prime power modulus
  • David Garth (Cochrane), 2000, Small limit points of sets of algebraic integers
  • Anwar Ayyad (Cochrane), 1997, The distribution of solutions of the multiplicative congruence x1x2...xn = c (mod p)
  • Idris Munshi (Smith), 1996, Orthogonality properties of mixed characters
  • Patrick Mitchell (Cochrane), 1995, Algorithms for finding small solutions
  • Roosbeh Vakil (Smith), 1992, A canonical combinatorial diagonalization of a subset of a finite integer lattice
  • Mohsen Taghavi (Smith), 1991, Lower bounds for the correlation coeficients of Rudin-Shapiro polynomials
  • Robert Girse (Chawla), 1979, Certain identities in partition theory
  • Paula Kemp (Maxfield), 1974, Properties of arithmetic functions of several variables
  • Jan Van der Lune (Dressler), 1973, Some observations in number theory and analysis
  • Sung-May Hsu Lee (Maxfield), 1971, The average order of the largest k-th divisors
  • C. Young (Chawla), 1971
  • Janina Spears (Cohen), 1970, Simultaneous binary compositions involving a pair of relatively l-free integers and a pair of integers, one of which is k-free and the other h-free
  • Chi-Dak Ngai Yeung (Maxfield), 1970, Some asymptotic formulas for the distribution of finite Abelian groups
  • Fuanglada Jung (Maxfield), 1969, The number of solutions of some systems of equations over a Galois field and an application to geometry

Former M.S. Students

  • Overtone Chipatala (Cochrane), 2016, Polygonal numbers
  • Joseph Sheppard (Pinner), 2016, The ABC Conjecture and its applications
  • Lance Kaminski (Pinner), 2009, A discussion of homogeneous quadratic equations
  • Ali Hakami (Cochrane), 2004, Factoring primes in quadratic number fields and primes of the form x^2+my^2
  • Christopher Elston (Cochrane), 2006, Sophie Germain primes
  • Justin Ostrander (Pinner), 2005, Elliptic curves & applications
  • Jeremy Coffelt (Pinner), 2005, Bounds on trinomial exponential sums
  • Angela Larson-Thome (Cochrane and Stromberg), 1995, Nowhere differentiable continuous functions
  • David Bishop (Cochrane and Dressler), 1991, The cryptologic significance of elliptic curves over finite fields