Results 21 to 30 of about 228 (50)

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

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   +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

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

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

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  

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

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

Finiteness of irreducible holomorphic eta quotients of a given level

, 2018
We show that for any positive integer N, there are only finitely many holomorphic eta quotients of level N, none of which is a product of two holomorphic eta quotients other than 1 and itself.
Bhattacharya, S.
core   +1 more source

Congruences for the Fishburn Numbers

, 2014
The Fishburn numbers, $\xi(n),$ are defined by a formal power series expansion $$ \sum_{n=0}^\infty \xi(n)q^n = 1 + \sum_{n=1}^\infty \prod_{j=1}^n (1-(1-q)^j). $$ For half of the primes $p$, there is a non--empty set of numbers $T(p)$ lying in $[0,p-1]$
Andrews, George E., Sellers, James A.
core