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.

Gathers clear and innovative chapters covering a wide range of subareas in number theory and algebraic geometry Reports on recent progress and open problems Features high-quality contributions by oft-underrepresented members of the math community

Autorentext

Ramla Abdellatif is an associate professor at Université de Picardie Jules Verne (Amiens, France). Her main research topic concerns the p-modular and p-adic Langlands correspondences for p-adic groups, which lie at the intersection of arithmetic geometry, representation theory and number theory, but she also has an interest in Lubin-Tate formal groups and effective aspects of Fontaine-Mazur conjecture. She has been involved in the Women in Numbers Europe conferences from the first edition: first as a group co-leader (2013), then as a group leader (2019) and last as an organiser (2022).
**Valentijn Karemaker is an assistant professor of mathematics at Utrecht University. She previously held positions at the University of Pennsylvania and Stockholm University. Her research is in arithmetic geometry, with a focus on arithmetic properties of (supersingular) abelian varieties in positive characteristic, Drinfeld modules and local-global principles. She has been a member of the Women in Numbers research network since the first European conference in 2013 and was an organiser of the WiNE IV conference in 2022.
**Lejla Smajlovi is a professor of mathematics at University of Sarajevo. Her research is in automorphic forms, with a focus on spectral properties of the Laplacian, the heat kernel and associated zeta and L-functions. She serves as a Managing Editor of the Journal of Number Theory and as a member of the Editorial Board of the Bulletin of the Malaysian Mathematical Sciences Society and Albanian Journal of Mathematics. She has been a member of the Women in Numbers research network since the first European conference in 2013 and will be an organiser of the WiNE V conference in 2025.

Inhalt

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.