Research Directions in Number Theory

This is an open access volume and it containscontains several number theory contributions, most of which were written in connection to the workshop WIN6: Women in Numbers, held in March 2023, at the Banff International Research Station (BIRS) in Banff, Alberta, Canada. The chapters comprise research outcomes from collaborations initiated during the workshop as well as other original research contributions. The volume also aims to introduce central research topics in number theory to advanced graduate students and recent PhDs. In this book, more background and details will be given than in standard journal papers. The workshop and this volume are part of the Women in Numbers network, aimed at highlighting the research of women in number theory as well as increasing their participation and bolstering collaborations of women mathematicians in number theory and related fields.

This book is open access, which means that you have free and unlimited access Part of the Women in Numbers network Highlights the research of women in number theory Presents new and original cutting-edge research

Klappentext
This is an open access volume and it contains several number theory contributions, most of which were written in connection to the workshop WIN6: Women in Numbers, held in March 2023, at the Banff International Research Station (BIRS) in Banff, Alberta, Canada. The chapters comprise research outcomes from collaborations initiated during the workshop as well as other original research contributions. The volume also aims to introduce central research topics in number theory to advanced graduate students and recent PhDs. In this book, more background and details will be given than in standard journal papers. The workshop and this volume are part of the Women in Numbers network, aimed at highlighting the research of women in number theory as well as increasing their participation and bolstering collaborations of women mathematicians in number theory and related fields.

Inhalt

Preface.- On rational points on classifying stacks and Malle's conjecture.- On a slice of the cubic 2-adic Mandelbrot set.- Towards a classification of $p^2$-discriminant ideal twins over number fields.- Generalized Eckardt points on Del Pezzo surfaces of degree 1.- Period-index in top cohomology over semiglobal fields.- On Invariants of ArtinSchreier Curves.- A Note on Large Sums of Divisor-Bounded Multiplicative Functions.- Prime and thickened prime components in Apollonian circle packings.- Machine learning for modular multiplication.- An explicit theta lift to Siegel paramodular forms.- Comparing densities for powers in Artin's conjecture on primitive roots.