Congruences for partial sums of the generating series for $\binom{3k}{k}$

We produce congruences modulo a prime $p > 3$ for sums $\sum_{k} (\binom{3 k}{k}) x^{k}$ over ranges $0 \leq k < q$ and $0 \leq k < q / 3$ , where $q$ is a power of $p$ . Here $x$ equals either $c^{2} / (1 - c)^{3}$ , or $4 s^{2} / (27 (s^{2} - 1))$ , where $c$ and $s$ are indeterminates. In the former case we deal more generally with shifted binomial coefficients $(\binom{3 k + e}{k})$ . Our method derives such congruences directly from closed forms for the corresponding series.

Congruences for partial sums of the generating series for $(\binom{3 k}{k})$

文献摘要

讨论

讲解博客

AI智能校验

Congruences for partial sums of the generating series for $(\binom{3 k}{k})$

文献摘要

讨论

讲解博客

AI智能校验

Congruences for partial sums of the generating series for (3kk)(k3k​)

文献摘要

讨论

|讲解博客

|AI智能校验

Congruences for partial sums of the generating series for (3kk)(k3k​)

文献摘要

讨论

|讲解博客

|AI智能校验

Congruences for partial sums of the generating series for $(\binom{3 k}{k})$

讲解博客

AI智能校验

Congruences for partial sums of the generating series for $(\binom{3 k}{k})$

讲解博客

AI智能校验