### Number Theory Group

#### Faculty

**Vorrapan (Fai) Chandee****Publications****Research Interests:**Analytic Number Theory, L-functions and Related Problems, Random Matrix Theory

**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

**Gerald Höhn****Publications****Research Interests:**Modular Forms, Automorphic Products, Moonshine

**Xiannan Li****Publications****Research Interests:**L-functions, Automorphic Forms, Prime Number Theory, Sieve Theory

**Christopher Pinner****Publications****Research Interests:**Mahler Measure and Lehmer's Problem, Exponential Sums, Diophantine Approximation

**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**Z**_{p}^{n}, 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 x_{1}x_{2}...x_{n}= 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