6 problems

Let $k,j,n$ be positive integers satisfying $n\equiv k\equiv j\equiv 0\pmod 2$, $j/2+n/2\equiv 1\pmod 2$, $k>n+1$, and $j>n-1$. Put … Let…

Let $k$ and $j$ be non-negative integers with $j$ even, $k\geq 3$, and $j\geq 4$. Let $f\in S_{2k+j-2}(SL_2(\mathbb Z))$ be a primitive form. Define … Suppose that a prime ideal…

Let $k$ and $j$ be non-negative integers with $j$ even and $k\geq 3$. Let $f=\sum a(n,f)q^n\in S_{2k+j-2}(SL_2(\mathbb Z))$ be a primitive form, and suppose that a sufficiently lar…

Let $\rho^\theta_\blambda$ be the $p$-adic realization of the motive associated with the Siegel modular form, let $rho^thetablambda aturaltheta$ denote its twist by $theta$, and le…

Let $\underline{k}=(k_1,k_2)$ with $k_1\ge k_2\ge3$, let $\mu_F(m)$ be the Dirichlet coefficients of the degree-$5$ standard $L$-function of $F$, and write…

Let $a\geq b\geq 0$ with $(a,b)\neq(0,0)$, let $V_{a,b}$ be the corresponding local system on $\A{2}$, let $T(p)$ be the Hecke operator at $p$, and let $S_{a-b,b+3}$ be the space o…