In transcendental number theory, a mathematical discipline, Baker's theorem gives a lower bound for the absolute value of linear combinations of logarithms...

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...

\ln \alpha } . It also would follow from the strengthened version of Baker's theorem above. The currently unproven four exponentials conjecture would also...

} The Gelfond–Schneider theorem answers affirmatively Hilbert's seventh problem. Lindemann–Weierstrass theorem Baker's theorem; an extension of the result...

theorem then follows by setting βij = 0 for every i and j, while the five exponentials theorem follows by setting x3 = γ/x1 and using Baker's theorem...

number of solutions of such equations. Nevertheless, a refinement of Baker's theorem by Feldman provides an effective bound: if x is an algebraic number...

exponential topics. Acoustic power Antilogarithm Apparent magnitude Baker's theorem Bel Benford's law Binary logarithm Bode plot Henry Briggs Bygrave slide...

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

Practically simultaneously, Alan Baker proved what we now know as Baker's theorem on linear forms in logarithms of algebraic numbers, which resolved...

analytic subgroup theorem is a significant result in modern transcendental number theory. It may be seen as a generalisation of Baker's theorem on linear forms...

non-zero algebraic for all 1 ≤ j ≤ n {\displaystyle 1\leq j\leq n} (by Baker's theorem). The trigonometric functions sin ⁡ ( x ) , cos ⁡ ( x ) , . . . {\displaystyle...

theory) ATS theorem (number theory) Auxiliary polynomial theorem (Diophantine approximation) Ax–Kochen theorem (number theory) Baker's theorem (number theory)...

proof of Baker's theorem contained such bounds, solving Gauss' class number problem for class number one in the process. This work won Baker the Fields...

studied by Gelfond and then solved by Alan Baker. It is called the Gelfond conjecture or Baker's theorem. Baker was awarded a Fields Medal in 1970 for this...

to prove asymptotic results such as Baker's theorem in transcendental number theory which was proved by Alan Baker (1966, 1967a, 1967b). In other cases...

between logarithms of algebraic numbers. But a conjectural extension of Baker's theorem implies that there should be no non-trivial algebraic relations between...

Gelfond–Schneider theorem. Alan Baker also used the method in the 1960s for his work on linear forms in logarithms and ultimately Baker's theorem. Another example...

and the cosine are transcendental numbers. This is a corollary of Baker's theorem, proved in 1966. If the sine of an angle is a rational number then...

(1999) calls this the Heegner theorem (cognate to Heegner points as in page xiii of Darmon (2004)) but omitting Baker's name is atypical.[inconsistent]Chowla...

Hall 2015 Theorem 5.3 Hall 2015 Example 3.41 Wei, James (October 1963). "Note on the Global Validity of the Baker-Hausdorff and Magnus Theorems". Journal...

particularly of Alan Baker, changed the position. Qualitatively speaking, Baker's theorems look weaker, but they have explicit constants and can actually be applied...

number field: Ax (1965) reduced the abelian case to a p-adic version of Baker's theorem, which was proved shortly afterwards by Brumer (1967). Mihăilescu (2009...

In mathematics, Roth's theorem or Thue–Siegel–Roth theorem is a fundamental result in diophantine approximation to algebraic numbers. It is of a qualitative...

results in some cases derive from Baker's method. Diophantine geometry Corvaja, P. and Zannier, U. "A subspace theorem approach to integral points on curves"...

approximately 180 publications in number theory, on subjects that included Baker's theorem, continued fractions, elliptic curves, regular languages, the integer...

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

In computational complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-complete...

Petersen–Morley Theorem I". Mathematical Proceedings of the Cambridge Philosophical Society. 30 (2): 192–196. doi:10.1017/S0305004100016601. Baker, H. F. (1935)...

Catalan's conjecture (or Mihăilescu's theorem) is a theorem in number theory that was conjectured by the mathematician Eugène Charles Catalan in 1844...

The Baire category theorem (BCT) is an important result in general topology and functional analysis. The theorem has two forms, each of which gives sufficient...