A Remark on Differences of Theta 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 the means of the number of divisors

‎We obtain the asymptotic expansion of the sequence with general term $frac{A_n}{G_n}$‎, ‎where $A_n$ and $G_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎Also‎, ‎we obtain some explicit bounds concerning $G_n$ and $frac{A_n}{G_n}$.

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

Theta hypergeometric series

We formulate general principles of building hypergeometric type series from the Jacobi theta functions that generalize the plain and basic hy-pergeometric series. Single and multivariable elliptic hypergeometric series are considered in detail. A characterization theorem for a single variable totally elliptic hypergeometric series is proved.

A short remark on the result of Jozsef Sandor

It is pointed out that, one of the results in the recently published article, ’On the Iyengar-Madhava Rao-Nanjundiah inequality and it’s hyperbolic version’ [3] by J´ozsef S´andor is logically incorrect and new corrected result with it’s proof is presented.