A remark on infinite series

A Remark on Eisenstein Series

The theory of Eisenstein series is fundamental for the spectral theory of automorphic forms. It was first developed by Selberg, and was completed by Langlands ([Lan76]; see also [MW95]). There are several known proofs for the meromorphic continuation of Eisenstein series (apart from very special cases of Eisenstein series which can be expressed in terms of Tate integrals). In all these proofs i...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Some Remarks on Infinite Series

In the present paper we investigate the following problems. Suppose an >O for n_-I and Z a,=-. n=1 N° 1. Does there exist a sequence of natural numbers No =O, Ni l-, such that it decomposes the series monotone decreasingly : In order to state the second problem we define the index nk (c) as the minimum m such that (2) Now the second problem is as follows. are equiconvergent. m kc a j. j=1 N° 2....

On Faster Convergent Infinite Series

Recommended by Laszlo Toth Suffcient conditions, necessary conditions for faster convergent infinite series, faster τ-convergent infinite series are studied. The faster convergence of infinite series of Kummer's type is proved. Copyright q 2008 Dušan Hoí y et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distributi...

Infinite Series

so π is an “infinite sum” of fractions. Decimal expansions like this show that an infinite series is not a paradoxical idea, although it may not be clear how to deal with non-decimal infinite series like (1.1) at the moment. Infinite series provide two conceptual insights into the nature of the basic functions met in high school (rational functions, trigonometric and inverse trigonometric funct...