A Note on Transcendental Power Series Mapping the Set of Rational Numbers into Itself
نویسندگان
چکیده
منابع مشابه
L - Series and Transcendental Numbers
This paper is a survey of some recent work of mine done jointly with V. Kumar Murty, N. Saradha, S. Gun and P. Rath. In all of these works, the motivating question is the following. Given an automorphic representation π , we consider the L-series L(s, π) attached to π according to the Langlands formalism. We are interested in the possible transcendence of special values L(k, π) when k is a posi...
متن کاملThere are less transcendental numbers than rational numbers
According to a basic theorem of transfinite set theory the set of irrational numbers is uncountable, while the set of rational numbers is countable. This is contradicted by the fact that any pair of irrational numbers is separated by at least one rational number. Hence, in the interval [0,1] there exist more rational numbers than irrational numbers.
متن کاملA note on commutative multivariate rational series
Direct arguments are presented showing that for rational series in several com muting variables the rational series problem is non computable and closure under Hadamard product fails
متن کاملOn Transcendental Numbers
Transcendental numbers play an important role in many areas of science. This paper contains a short survey on transcendental numbers and some relations among them. New inequalities for transcendental numbers are stated in Section 2 and proved in Section 4. Also, in relationship with these topics, we study the exponential function axioms related to the Yang-Baxter equation.
متن کاملA Note on the Strong Law of Large Numbers
Petrov (1996) proved the connection between general moment conditions and the applicability of the strong law of large numbers to a sequence of pairwise independent and identically distributed random variables. This note examines this connection to a sequence of pairwise negative quadrant dependent (NQD) and identically distributed random variables. As a consequence of the main theorem ...
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: Communications in Mathematics
سال: 2017
ISSN: 2336-1298
DOI: 10.1515/cm-2017-0001