TY - BOOK ID - 145732905 TI - Number Theory and Symmetry PY - 2020 PB - Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute DB - UniCat KW - Research & information: general KW - Mathematics & science KW - quantum computation KW - IC-POVMs KW - knot theory KW - three-manifolds KW - branch coverings KW - Dehn surgeries KW - zeta function KW - Pólya-Hilbert conjecture KW - Riemann interferometer KW - prime numbers KW - Prime Number Theorem (P.N.T.) KW - modified Sieve procedure KW - binary periodical sequences KW - prime number function KW - prime characteristic function KW - limited intervals KW - logarithmic integral estimations KW - twin prime numbers KW - free probability KW - p-adic number fields ℚp KW - Banach ∗-probability spaces KW - C*-algebras KW - semicircular elements KW - the semicircular law KW - asymptotic semicircular laws KW - Kaprekar constants KW - Kaprekar transformation KW - fixed points for recursive functions KW - Baker’s theorem KW - Gel’fond–Schneider theorem KW - algebraic number KW - transcendental number KW - standard model of elementary particles KW - 4-manifold topology KW - particles as 3-Braids KW - branched coverings KW - knots and links KW - charge as Hirzebruch defect KW - umbral moonshine KW - number of generations KW - the pe-Pascal’s triangle KW - Lucas’ result on the Pascal’s triangle KW - congruences of binomial expansions KW - primality test KW - Miller–Rabin primality test KW - strong pseudoprimes KW - primality witnesses KW - quantum computation KW - IC-POVMs KW - knot theory KW - three-manifolds KW - branch coverings KW - Dehn surgeries KW - zeta function KW - Pólya-Hilbert conjecture KW - Riemann interferometer KW - prime numbers KW - Prime Number Theorem (P.N.T.) KW - modified Sieve procedure KW - binary periodical sequences KW - prime number function KW - prime characteristic function KW - limited intervals KW - logarithmic integral estimations KW - twin prime numbers KW - free probability KW - p-adic number fields ℚp KW - Banach ∗-probability spaces KW - C*-algebras KW - semicircular elements KW - the semicircular law KW - asymptotic semicircular laws KW - Kaprekar constants KW - Kaprekar transformation KW - fixed points for recursive functions KW - Baker’s theorem KW - Gel’fond–Schneider theorem KW - algebraic number KW - transcendental number KW - standard model of elementary particles KW - 4-manifold topology KW - particles as 3-Braids KW - branched coverings KW - knots and links KW - charge as Hirzebruch defect KW - umbral moonshine KW - number of generations KW - the pe-Pascal’s triangle KW - Lucas’ result on the Pascal’s triangle KW - congruences of binomial expansions KW - primality test KW - Miller–Rabin primality test KW - strong pseudoprimes KW - primality witnesses UR - https://www.unicat.be/uniCat?func=search&query=sysid:145732905 AB - 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. ER -