Introduction to Transcendental Numbers

  title={Introduction to Transcendental Numbers},
  author={Serge Lang},

A note on special values of $L$-functions

In this paper, we link the nature of special values of certain Dirichlet L-functions to those of multiple gamma values.

Meromorphic Maps on Riemann Surfaces and Transcendence1

A Refined Criterion for Schanuel’s Conjecture

We extend the range of validity for the parameters in the equivalence between Roy’s Conjecture and Schanuel’s Conjecture.

On a conjecture of Graham on the p-divisibility of central binomial coefficients

We show that for every r ≥ 1, and all r distinct (sufficiently large) primes p1, ..., pr > p0(r), there exist infinitely many integers n such that

Connections Between Transcendence Degree and Diophantine Estimates

We state two conjectures, which together would yield strong results of algebraic independence related to Schanuel’s Conjecture. Partial results on these conjectures are also discussed. 1991

On a Problem of Alaoglu and Erdős

Starting with an elementary problem that appeared in the Putnam mathematics competition, we proceed to discuss some techniques of transcendental number theory and prove the following result. If p, q,

Analytic and pseudo-analytic structures

The logical roots in the case of model theoretic geometric stability theory are not only clear but also remain very important in all its applications.

J ul 2 01 1 Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles Dedicated to Fabrizio Cantanese

The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry. When the jet values are prescribed on a positive dimensional



Einführung in die transzendenten Zahlen

Uber transzendente Zahlen gibt es nur sehr wenige zusammenfassende Darstellungen. Ein Grund dafiir diirfte darin zu suchen sein, daB in der Originalliteratur iiber transzendente Zahlen nur vereinzelt

Über transzendente $P$-adische Zahlen

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A transcendence measure for E -functions

Siegel defined an E -function to be a function which admits a power series expansion with complex coefficients β n , belonging to some algebraic number field K (of finite degree over the rationals

Ueber die Zahl π.*)

Bei der Vergeblichkeit der so ausserordentlich zahlreichen Versuche**), die Quadratur des Kreises mit Cirkel und Lineal auszufuhren, halt man allgemein die Losung der bezeichneten Aufgabe fur