On homomorphic encryption using abelian groups: Classical security analysis -- A survey of local-global methods for Hilbert’s Tenth Problem -- Sums of proper divisors with missing digits -- Rational approximations, multidimensional continued fractions and lattice reduction -- Campana points on diagonal hypersurfaces -- Power values of power sums: A survey -- Transcendence measure of e^{1/n} -- Real quadratic singular moduli and p-adic families of modular forms -- Elliptic fibrations and involutions on K3 surfaces -- Mirror constructions for K3 surfaces from bimodal singularities -- Variants of the Li-type criteria for the Generalized Riemann hypothesis -- A note on the non-vanishing of Poincaré series.

This volume contains research and expository content based on a wide variety of topics within modern number theory and arithmetic geometry. Research in this volume arises from or is connected with the Women in Numbers Europe (WiNE) IV conference held in Summer 2022 in Utrecht, The Netherlands. The contents of this volume are of interest to professional mathematicians, graduate students, and researchers working in number theory, arithmetic geometry, and related areas.