Results 11 to 20 of about 226 (52)

Some theorems on the explicit evaluation of Ramanujan′s theta‐functions

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 40, Page 2149-2159, 2004., 2004
Bruce C. Berndt et al. and Soon‐Yi Kang have proved many of Ramanujan′s formulas for the explicit evaluation of the Rogers‐Ramanujan continued fraction and theta‐functions in terms of Weber‐Ramanujan class invariants. In this note, we give alternative proofs of some of these identities of theta‐functions recorded by Ramanujan in his notebooks and ...
Nayandeep Deka Baruah, P. Bhattacharyya
wiley   +1 more source

Dedekind's eta-function and Rogers-Ramanujan identities

, 2010
We prove a q-series identity that generalises Macdonald's A_{2n}^{(2)} eta-function identity and the Rogers-Ramanujan identities. We conjecture our result to generalise even further to also include the Andrews-Gordon identities.Comment: 14 ...
Warnaar, S. Ole, Zudilin, Wadim
core   +1 more source

Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8

Open Mathematics
In this article, we compute binomial convolution sums of divisor functions associated with the Dirichlet character modulo 8, which is the remaining primitive Dirichlet character modulo powers of 2 yet to be considered.
Jin Seokho, Park Ho
doaj   +1 more source

Relations for Bernoulli--Barnes Numbers and Barnes Zeta Functions

, 2013
The \emph{Barnes $\zeta$-function} is \[ \zeta_n (z, x; \a) := \sum_{\m \in \Z_{\ge 0}^n} \frac{1}{\left(x + m_1 a_1 + \dots + m_n a_n \right)^z} \] defined for $\Re(x) > 0$ and $\Re(z) > n$ and continued meromorphically to $\C$.
Bayad, Abdelmejid, Beck, Matthias
core   +2 more sources

A study on a type of degenerate poly-Dedekind sums

Demonstratio Mathematica
Dedekind sums and their generalizations are defined in terms of Bernoulli functions and their generalizations. As a new generalization of the Dedekind sums, the degenerate poly-Dedekind sums, which are obtained from the Dedekind sums by replacing ...
Ma Yuankui, Luo Lingling, Kim Taekyun, Li Hongze, Zhang Wenpeng   +4 more
doaj   +1 more source

On Eisenstein series in $M_{2k}(\Gamma_0(N))$ and their applications

, 2018
Let $k,N \in \mathbb{N}$ with $N$ square-free and $k>1$. We prove an orthogonal relation and use this to compute the Fourier coefficients of the Eisenstein part of any $f(z) \in M_{2k}(\Gamma_0(N))$ in terms of sum of divisors function. In particular, if
Aygin, Zafer Selcuk
core   +1 more source

The hybrid power mean involving the Kloosterman sums and Dedekind sums

Open Mathematics
Kloosterman sums and Dedekind sums are two important sums in analytic number theory, the study of their various properties is a very interesting subject.
Li Ruiyang, Chen Long
doaj   +1 more source

Finiteness of simple holomorphic eta quotients of a given weight

, 2016
We provide a simplified proof of Zagier's conjecture / Mersmann's theorem which states that of any particular weight, there are only finitely many holomorphic eta quotients, none of which is an integral rescaling of another eta quotient or a product of ...
Bhattacharya, Soumya
core   +1 more source

Rademacher-Carlitz Polynomials [PDF]

, 2013
We introduce and study the \emph{Rademacher-Carlitz polynomial} \[ \RC(u, v, s, t, a, b) := \sum_{k = \lceil s \rceil}^{\lceil s \rceil + b - 1} u^{\fl{\frac{ka + t}{b}}} v^k \] where $a, b \in \Z_{>0}$, $s, t \in \R$, and $u$ and $v$ are variables ...
Beck, Matthias, Kohl, Florian
core  

Ray class invariants over imaginary quadratic fields

, 2011
Let $K$ be an imaginary quadratic field of discriminant less than or equal to -7 and $K_{(N)}$ be its ray class field modulo $N$ for an integer $N$ greater than 1.
Jung, Ho Yun, Koo, Ja Kyung, Shin, Dong Hwa   +2 more
core   +1 more source