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Number Theory and Symmetry
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According to Carl Friedrich Gauss (1777–1855), mathematics is the queen of the sciences—and number theory is the queen of mathematics. Numbers (integers, algebraic integers, transcendental numbers, p-adic numbers) and symmetries are investigated in the nine refereed papers of this MDPI issue. This book shows how symmetry pervades number theory. In particular, it highlights connections between symmetry and number theory, quantum computing and elementary particles (thanks to 3-manifolds), and other branches of mathematics (such as probability spaces) and revisits standard subjects (such as the Sieve procedure, primality tests, and Pascal’s triangle). The book should be of interest to all mathematicians, and physicists.
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Keywords
- 4-manifold topology
- algebraic number
- asymptotic semicircular laws
- Baker’s theorem
- Banach ∗-probability spaces
- binary periodical sequences
- branch coverings
- branched coverings
- C*-algebras
- charge as Hirzebruch defect
- congruences of binomial expansions
- Dehn surgeries
- fixed points for recursive functions
- free probability
- Gel’fond–Schneider theorem
- IC-POVMs
- Kaprekar constants
- Kaprekar transformation
- Knot theory
- knots and links
- limited intervals
- logarithmic integral estimations
- Lucas’ result on the Pascal’s triangle
- Mathematics & science
- Miller–Rabin primality test
- modified Sieve procedure
- number of generations
- p-adic number fields ℚp
- particles as 3-Braids
- Pólya-Hilbert conjecture
- primality test
- primality witnesses
- prime characteristic function
- prime number function
- Prime Number Theorem (P.N.T.)
- Prime Numbers
- quantum computation
- Reference, information & interdisciplinary subjects
- Research & information: general
- Riemann interferometer
- semicircular elements
- standard model of elementary particles
- strong pseudoprimes
- the pe-Pascal’s triangle
- the semicircular law
- three-manifolds
- transcendental number
- twin prime numbers
- umbral moonshine
- Zeta function
Links
DOI: 10.3390/books978-3-03936-687-3Editions