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In contrast to all other known Ramanujan-type congruences, we discover that Ramanujan-type congruences for Hurwitz class numbers can be supported on non-holomorphic generating series. We establish a divisibility result for such non-holomorphic congruences of Hurwitz class numbers. The two keys tools in our proof are the holomorphic projection of products of theta series with a Hurwitz class number generating series and a theorem by Serre, which allows us to rule out certain congruences.
Let $lambda$ be an integer, and $f(z)=sum_{ngg-infty} a(n)q^n$ be a weakly holomorphic modular form of weight $lambda+frac 12$ on $Gamma_0(4)$ with integral coefficients. Let $ellgeq 5$ be a prime. Assume that the constant term $a(0)$ is not zero mod
The sequence $A(n)_{n geq 0}$ of Apery numbers can be interpolated to $mathbb{C}$ by an entire function. We give a formula for the Taylor coefficients of this function, centered at the origin, as a $mathbb{Z}$-linear combination of multiple zeta valu
This paper is concerned with a class of partition functions $a(n)$ introduced by Radu and defined in terms of eta-quotients. By utilizing the transformation laws of Newman, Schoeneberg and Robins, and Radus algorithms, we present an algorithm to find
Let $p$ be a prime with $p>3$, and let $a,b$ be two rational $p-$integers. In this paper we present general congruences for $sum_{k=0}^{p-1}binom akbinom{-1-a}kfrac p{k+b}pmod {p^2}$. For $n=0,1,2,ldots$ let $D_n$ and $b_n$ be Domb and Almkvist-Zudil
We define a new kind of classical digamma function, and establish its some fundamental identities. Then we apply the formulas obtained, and extend tools developed by Flajolet and Salvy to study more general Euler type sums. The main results of Flajol