Book Review: Transcendental number theory
نویسندگان
چکیده
منابع مشابه
Auxiliary functions in transcendental number theory
We discuss the role of auxiliary functions in the development of transcendental number theory. Earlier auxiliary functions were completely explicit (§ 1). The earliest transcendence proof is due to Liouville (§ 1.1), who produced the first explicit examples of transcendental numbers at a time where their existence was not yet known; in his proof, the auxiliary function is just a polynomial in o...
متن کاملOn Ramachandra’s Contributions to Transcendental Number Theory
The title of this lecture refers to Ramachandra’s paper in Acta Arithmetica [36], which will be our central subject: in section 1 we state his Main Theorem, in section 2 we apply it to algebraically additive functions. Next we give new consequences of Ramachandra’s results to density problems; for instance we discuss the following question: let E be an elliptic curve which is defined over the f...
متن کاملThe role of complex conjugation in transcendental number theory
In his two well known 1968 papers “Contributions to the theory of transcendental numbers”, K. Ramachandra proved several results showing that, in certain explicit sets {x1, . . . , xn} of complex numbers, one element at least is transcendental. In specific cases the number n of elements in the set was 2 and the two numbers x1, x2 were both real. He then noticed that the conclusion is equivalent...
متن کاملFrom highly composite numbers to transcendental number theory
In a well–known paper published in 1915 in the Proceedings of the London Mathematical Society, Srinivasa Ramanujan defined and studied highly composite numbers. A highly composite number is a positive integer n with more divisors than any positive integer smaller than n. This work was pursued in 1944 by L. Alaoglu and P. Erdős, who raised a question which belongs to transcendental number theory...
متن کاملMath 249 A Fall 2010 : Transcendental Number Theory
α is algebraic if there exists p ∈ Z[x], p 6= 0 with p(α) = 0, otherwise α is called transcendental . Cantor: Algebraic numbers are countable, so transcendental numbers exist, and are a measure 1 set in [0, 1], but it is hard to prove transcendence for any particular number. Examples of (proported) transcendental numbers: e, π, γ, e, √ 2 √ 2 , ζ(3), ζ(5) . . . Know: e, π, e, √ 2 √ 2 are transce...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1978
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1978-14584-4