5 problems

Let ${\mathcal {X}}$ be a $\widehat{\Gamma}$-orbit of algebraic Hecke characters over $K$, and let ${\mathcal {L}}(\lambda)$ denote the normalized algebraic Hecke $L$-value defined…

Let $f$ be an eigenform that is non-exceptional in the sense of Cornut and Vatsal. Let $K$ be an imaginary quadratic field, let $p$ be a prime, and let $\chi$ range over ring class…

For a nonzero Laurent polynomial $P$, let its logarithmic Mahler measure be … Let $f$ be the modular form appearing in the surrounding discussion, and consider the four-variable po…

Let $P_t=(1+x_1+x_2+x_3)(1+x_1^{-1}+x_2^{-1}+x_3^{-1})-t$ be the one-parameter family of Laurent polynomials, and consider the Feynman integral associated to $P_1$. Let $f$ be a cu…

Let $(p,k)$ be an irregular pair with $k$ even and $k\geq 12$. Let $F={\bf Q}(\mu_p)$, let $A_F^{(1-k)}$ be the corresponding eigenspace of the $p$-part of the class group, and let…