Search results
Results from the WOW.Com Content Network
A more recent proof by Wadim Zudilin is more reminiscent of Apéry's original proof, [6] and also has similarities to a fourth proof by Yuri Nesterenko. [7] These later proofs again derive a contradiction from the assumption that ζ ( 3 ) {\displaystyle \zeta (3)} is rational by constructing sequences that tend to zero but are bounded below by ...
ζ(3) was named Apéry's constant after the French mathematician Roger Apéry, who proved in 1978 that it is an irrational number. [4] This result is known as Apéry's theorem. The original proof is complex and hard to grasp, [5] and simpler proofs were found later. [6]
In 1947 Apéry was appointed Maître de conférences (lecturer) at the University of Rennes. In 1949 he was appointed Professor at the University of Caen, where he remained until his retirement. In 1979 he published an unexpected proof of the irrationality of ζ, which is the sum of the inverses of the cubes of the positive integers. An ...
Anne's theorem ; Apéry's theorem (number theory) Apollonius's theorem (plane geometry) Appell–Humbert theorem (complex manifold) Arakelyan's theorem (complex analysis) Area theorem (conformal mapping) (complex analysis) Arithmetic Riemann–Roch theorem (algebraic geometry) Aronszajn–Smith theorem (functional analysis)
Apéry's constant arises naturally in a number of physical problems, including in the second- and third-order terms of the electron's gyromagnetic ratio, computed using quantum electrodynamics. [ 9 ] ζ ( 3 ) {\displaystyle \zeta (3)} is known to be an irrational number which was proven by the French mathematician Roger Apéry in 1979.
It is known that ζ(3) is irrational (Apéry's theorem) and that infinitely many of the numbers ζ(2n + 1) : n ∈ , are irrational. [1] There are also results on the irrationality of values of the Riemann zeta function at the elements of certain subsets of the positive odd integers; for example, at least one of ζ (5), ζ (7), ζ (9), or ζ ...
Sometimes called a "budget letter" or proof of income letter, the benefit verification statement from Social Security is used for several different instances where proof of your status or income is...
The first rigorous proof was published by Argand in 1806. Dirichlet's theorem on arithmetic progressions. In 1808 Legendre published an attempt at a proof of Dirichlet's theorem, but as Dupré pointed out in 1859 one of the lemmas used by Legendre is false. Dirichlet gave a complete proof in 1837.