Results 11 to 20 of about 207 (34)

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

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

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

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

Taylor coefficients of non-holomorphic Jacobi forms and applications

, 2017
In this paper, we prove modularity results of Taylor coefficients of certain non-holomorphic Jacobi forms. It is well-known that Taylor coefficients of holomorphic Jacobi forms are quasimoular forms.
Bringmann, Kathrin
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

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

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  

A Framework for Modular Properties of False Theta Functions

, 2019
False theta functions closely resemble ordinary theta functions, however they do not have the modular transformation properties that theta functions have.
Bringmann, Kathrin, Nazaroglu, Caner
core   +1 more source