16 problems

Let $S=S(a,b,c;n)$ be the summand obtained from the WZ pair in the harmonic extension of the displayed Ramanujan $1/\pi$-series, and let $V_N(S)$ be the span of the coefficients of…

Let $S_1,S_2,S_3$ be the three summands obtained from the WZ seeds used to construct harmonic extensions of the displayed Ramanujan $1/\pi$-formula, and let $V_N(S_i)$ denote the s…

Let … The two displayed series are conjectured to converge to the stated multiples of $1/\pi$. Sun's 1/pi series conjecture. … and … The source presents these as open conjectures m…

PSLQ conjecture. The coefficients and multiplier are conjectured to be

Sun's new double-binomial series conjecture.

Sun's double-binomial series conjecture.

Sun's $F_k(-324)$ series conjecture.

Let $W_k(x)=\sum_{j=0}^k\binom{k}{j}\binom{k+j}{j}\binom{2j}{j}\binom{2(k-j)}{k-j}x^j$. Sun's $W_k(9/10)$ congruence conjecture. (i) For any $n\in\mathbb Z_{>0}$, … (ii) If…

Russell's conjecture for level 2. There exists a polynomial $P(u,v)$ of degree $(p+1)/2$ in $u$ and $v$ such that

Let $p$ be a prime, let $(a)_n$ denote the rising factorial, let $\left(\frac{-23}{p}\right)$ be the Legendre symbol, and let $L_{-23,p}(2)$ denote the $p$-adic $L$-value. Guillera…

Let $p$ be a prime, let $(a)_n$ denote the rising factorial, and let $\zeta_p(k)$ denote the $p$-adic analogue of the zeta value $\zeta(k)$. The coefficients $r_2,r_4,r_5,\ldots$ a…

Let $p$ be a positive odd number, and let $B(n,x)$, $v_0$, $m$, $j$, $\beta_k$, $\beta_k$, $\beta_k$, $\beta_k$, $\beta_k$, $\beta_k$, $\beta_k$, $\beta_k$, $\beta_k$, $\beta_k$,…

Modular-identity conjecture. If one of the relations

Monodromy-matrix conjecture. The monodromy matrix around $z=z_c$ is

Guillera–Almkvist conjecture. The quantities $r$, $\alpha_0$, and $\tau_0^2$ are rational if and only if $z_0$, $c_0$, $b_0$, and $a_0$ are algebraic.

Let $T_{2k}(b,1)$ be the trinomial coefficient polynomial used in the paper. Consider identities … where $a_0,a_1,m\in\mathbb Z$, $b\in\{1,3,4,\ldots\}$, $a_1>0$, and $C^2$ is posi…