The irrationality of some number theoretical series
Transcendental numbers having explicit -adic and Jacobi-Perron expansions
Two theorems on meromorphic functions used as a principle for proofs on irrationality
In this paper we discuss two theorems on meromorphic functions of Nikishin and Chudnovsky. Our purpose is to show, how to derive some well-known but not obvious results on irrationality in a systematic and simple way from properties of meromorphic functions with arithmetic conditions. As far as it stands, we have no new results on irrationality, to the contrary some results on numbers of the corollaries are known already since a long time to be transcendental (cf. [4], [9] and [10]). Our main intention...
Über lineare Unabhängigkeit.
Über verschwindende Summen von Einheitswurzeln.
Ueber arithmetische Eigenschaften gewisser transcendenter Functionen, II
Ueber Irrationalität von Reihen.
Valeurs entières de fractions rationnelles
Verscharfung eines Arithmetischen Satzes von Tschakaloff
Well-poised hypergeometric service for diophantine problems of zeta values
It is explained how the classical concept of well-poised hypergeometric series and integrals becomes crucial in studying arithmetic properties of the values of Riemann’s zeta function. By these well-poised means we obtain: (1) a permutation group for linear forms in and yielding a conditional upper bound for the irrationality measure of ; (2) a second-order Apéry-like recursion for and some low-order recursions for linear forms in odd zeta values; (3) a rich permutation group for a family...
Zur linearen Unabhängigkeit von Quadratwurzeln über den rationalen Zahlen.
О линейной независимости значений целых гипергеометрических функций с иррациональными параметрами
Об арифметических свойствах значений гипергеометрических функций