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Derivatives of theta functions as Traces of Partition Eisenstein series
Tewodros Amdeberhan, Ken Ono, Ajit Singh
In his "lost notebook'', Ramanujan used iterated derivatives of two theta functions to define sequences of -series and that he claimed to be quas…
Eichler-Selberg relations for singular moduli
Yuqi Deng, Toshiki Matsusaka, Ken Ono
The Eichler-Selberg trace formula expresses the trace of Hecke operators on spaces of cusp forms as weighted sums of Hurwitz-Kronecker class numbers. We extend this formula to a na…
A note on odd partition numbers
Michael Griffin, Ken Ono
Ramanujan's celebrated partition congruences modulo assert that where satisfies $24δ_{\ell}\eq…
MacMahon's sums-of-divisors and allied -series
Tewodros Amdeberhan, Ken Ono, Ajit Singh
Here we investigate the -series \begin{align*} \mathcal{U}_a(q)&=\sum_{n=0}^{\infty} MO(a;n)q^n&:=\sum_{0< k_1<k_2<\cdots<k_a} \frac{q^{k_1+k_2+\cdots+k_a}}{(1-q^{k_1})^2(1-q^{k…
Hypergeometry and the AGM over Finite Fields
Eleanor McSpirit, Ken Ono
One of the most celebrated applications of Gauss' hypergeometric functions is in connection with the rapid convergence of sequences and special values that arise in the the…
Counting matrix points on certain varieties over finite fields
Yifeng Huang, Ken Ono, Hasan Saad
Classical hypergeometric functions are well-known to play an important role in arithmetic algebraic geometry. These functions offer solutions to ordinary differential equations, an…