In mathematics, the Gelfond–Schneider theorem establishes the transcendence of a large class of numbers. It was originally proved independently in 1934...

in 1930. In 1934, Aleksandr Gelfond and Theodor Schneider independently proved the more general Gelfond–Schneider theorem, which solved the part of Hilbert's...

is both irrational and transcendental. This follows from the Gelfond–Schneider theorem, which establishes ab to be transcendental, given that a is algebraic...

mathematician. Gelfond's theorem, also known as the Gelfond–Schneider theorem, is named after him. Alexander Gelfond was born in Saint Petersburg, Russian Empire...

{\displaystyle 2^{\sqrt {2}}} and Gelfond's constant e π {\displaystyle e^{\pi }} . The Gelfond–Schneider theorem follows from Schanuel's conjecture...

notation, Baker's theorem is a nonhomogeneous generalization of the Gelfond–Schneider theorem. Specifically it states: Baker's Theorem—If λ 1 , … , λ n...

values of meromorphic functions. The theorem implies both the Hermite–Lindemann and Gelfond–Schneider theorems, and implies the transcendence of some...

more general statement in 1885. The theorem, along with the Gelfond–Schneider theorem, is extended by Baker's theorem, and all of these would be further...

transcendental? The affirmative answer was provided in 1934 by the Gelfond–Schneider theorem. This work was extended by Alan Baker in the 1960s in his work...

lemma. This result, the Gelfond–Schneider theorem, proved the transcendence of numbers such as eπ and the Gelfond–Schneider constant. The next big result...

problem in his PhD thesis, which then came to be known as the Gelfond–Schneider theorem. Later, he became an assistant to Carl Ludwig Siegel in Göttingen...

mathematicians, including Alexander Gelfond and Theodor Schneider who used it independently to prove the Gelfond–Schneider theorem. Alan Baker also used the method...

Aleksandr Gelfond in 1934, and refined by Theodor Schneider in 1935. This result is known as Gelfond's theorem or the Gelfond–Schneider theorem. (The restriction...

The logarithm is an example of a transcendental function. The Gelfond–Schneider theorem asserts that logarithms usually take transcendental, i.e. "difficult"...

Franel–Landau theorem (number theory) Gelfond–Schneider theorem (transcendental number theory) Glaisher's theorem (number theory) Green–Tao theorem (number...

{E}}(2^{x})=\mathbb {Q} ,} This result is a corollary of the Gelfond–Schneider theorem, which states that if α ≠ 0 , 1 {\displaystyle \alpha \neq 0,1}...

the Gelfond–Schneider theorem shows that 2 {\displaystyle {\sqrt {2}}} 2 {\displaystyle {\sqrt {2}}} is transcendental, hence irrational. This theorem states...

the Gelfond–Schneider theorem, but this fact is irrelevant to the correctness of the non-constructive proof. A constructive proof of the theorem that...

with any algebraic numerical coefficients 12. Extensions of Kronecker's theorem on Abelian fields to any algebraic realm of rationality 13. Impossibility...

vector space. Baker's theorem Dehn invariant Gelfond–Schneider theorem Hamel basis Hodge conjecture Lindemann–Weierstrass theorem Linear flow on the torus...

the National Academy of Sciences, India. Baker generalised the Gelfond–Schneider theorem, which itself is a solution to Hilbert's seventh problem. Specifically...

first-ever IMU silver plaque in recognition of his proof of Fermat's Last Theorem. Don Zagier referred to the plaque as a "quantized Fields Medal". Accounts...

irrational (that is, not rational), and both b and x are algebraic, Gelfond–Schneider theorem asserts that all values of bx are transcendental (that is, not...

transcendental number theory, in which a major result is the Gelfond–Schneider theorem, and a major open question is Schanuel's conjecture. For purposes...

Proof that e is irrational Lindemann–Weierstrass theorem Hilbert's seventh problem Gelfond–Schneider theorem Erdős–Borwein constant Liouville number Irrationality...

the functions, however, is optional. Using the Gelfond–Schneider theorem and Lindemann–Weierstrass theorem, many of the standard elementary functions can...

6651441426902251886502972498731\ldots } is transcendental. See Gelfond–Schneider theorem for later developments. He is also known for the Kusmin-Landau...

{\sqrt[{\infty }]{2}}_{s}=2^{1/2}={\sqrt {2}}} . It follows from the Gelfond–Schneider theorem that super-root n s {\displaystyle {\sqrt {n}}_{s}} for any positive...

transcendental (which is already known, by consequence of the Gelfond–Schneider theorem). An open problem in number theory settled by the conjecture is...

is not algebraic if 1 < a {\textstyle 1<a} is algebraic by the Gelfond–Schneider theorem. Consequently, the class of formally exponential fields is not...