Lateral Movement in Undergraduate Research: Case Studies in Number Theory

DOI10.1007/978-3-030-37853-0_7zbMath1441.11001OpenAlexW3016333832MaRDI QIDQ5118418

Publication date: 8 September 2020

Published in: Foundations for Undergraduate Research in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-37853-0_7

Mathematics Subject Classification ID

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory (11-01)

Cites Work

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Supercharacters, exponential sums, and the uncertainty principle.
Unitary equivalence to a complex symmetric matrix: low dimensions
Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs
Spectral and computational properties of band symmetric Toeplitz matrices
Visual properties of generalized Kloosterman sums
The cyclotomy of finite commutative P.I.R.'s
Chebotarëv and his density theorem
On algebras related to the discrete cosine transform
On the $p$-adic denseness of the quotient set of a polynomial image
Primitive root biases for prime pairs. I: Existence and non-totality of biases
A supercharacter approach to Heilbronn sums
An uncertainty principle for cyclic groups of prime order
Basic characters of the unitriangular group
On the closure of the complex symmetric operators: compact operators and weighted shifts
On the matrix equation $XA+AX^T=0$
Primitive root bias for twin primes. II: Schinzel-type theorems for totient quotients and the sum-of-divisors function
Ramanujan sums as supercharacters
$p$-adic denseness of members of partitions of $\mathbb{N}$ and their ratio sets
The primes contain arbitrarily long arithmetic progressions
Supercharacters, elliptic curves, and the sixth moment of Kloosterman sums
On the matrix equation $XA + AX^T = 0$. II: Type 0-I interactions
$p$-adic quotient sets. II: Quadratic forms
Basic characters of the unitriangular group (for arbitrary primes)
JMM Lecture Sampler
ON HEILBRONN'S EXPONENTIAL SUM
Unitary equivalence to a complex symmetric matrix: a modulus criterion
Quotient Sets and Diophantine Equations
On the Difference in Values of the Euler Totient Function Near Prime Arguments
A Heuristic Asymptotic Formula Concerning the Distribution of Prime Numbers
Variational principles for symmetric bilinear forms
Unitary equivalence to a complex symmetric matrix: geometric criteria
Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116)
Quotients of Primes
Asymptotic density of A⊂ ℕ and density of the ratio set R(A)
Quotients of Fibonacci Numbers
Supercharacters and the discrete Fourier, cosine, and sine transforms
Answers to Two Questions Concerning Quotients of Primes
On the norm closure problem for complex symmetric operators
THE QUOTIENT SET OF -GENERALISED FIBONACCI NUMBERS IS DENSE IN
The graphic nature of Gaussian periods
$p$-adic quotient sets
Primitive Root Bias for Twin Primes
Unitary equivalence to a truncated Toeplitz operator: analytic symbols
Two remarks about nilpotent operators of order two
Quotients of Gaussian Primes
Upper and Lower Semimodularity of the Supercharacter Theory Lattices of Cyclic Groups
The Graphic Nature of the Symmetric Group
Supercharacters and superclasses for algebra groups
Four Quotient Set Gems
On ratio sets of natural numbers
On Some Exponential Sums
The basic character table of the unitriangular group

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