Format: Hardback, 217 pages, height x width: 235x155 mm, 2 Illustrations, color;
20 Illustrations, black and white; X, 217 p. 22 illus., 2 illus. in color.
Series: University Texts in the Mathematical Sciences
Pub. Date: 13-Apr-2024
ISBN-13: 9789819996018
This book serves as an illuminating introduction to the intricacies of the geometry of numbers. It commences by exploring basic concepts of convex sets and lattices in Euclidean space and goes on to delve into Minkowskis fundamental theorem for convex bodies and its applications. It discusses critical determinants and successive minima before explaining the core results of packings and coverings. The text goes on to delve into the significance of renowned conjectures such as Minkowskis conjecture regarding the product of linear forms, Watsons conjecture, and the conjecture of Bambah, Dumir, and Hans-Gill concerning non-homogeneous minima of indefinite quadratic forms.
Dedicated to Prof. R.P. Bambah on his 98th birthday, a living legend of number theory in India, this comprehensive book addresses both homogeneous and non-homogeneous problems, while sprinkling in historical insights and highlighting unresolved questions in the field. It is ideally suited for beginners embarking on self-study as well as for use as a text for a one- or two-semester introductory course. Professor
1. Preliminaries.-
2. Minkowski's Fundamental Theorem and its Applications.-
3. Lattices.-
4. Minima of Positive De nite Quadratic Forms.-
5. Critical Determinant.-
6. Successive Minima.-
7. Packings Density.-
8. Coverings.-
9. Homogeneous Minimum.-
10. Inhomogeneous Problems.
Format: Hardback, 470 pages, height x width: 235x155 mm, X, 470 p.
Series: Vita Mathematica 21
Pub. Date: 29-Mar-2024
ISBN-13: 9783031521348
Felix Hausdorff is a singular phenomenon in the history of science. As a mathematician, he played a major role in shaping the development of modern mathematics in the 20th century. He founded general topology as an independent mathematical discipline, while enriching set theory with a number of fundamental concepts and results. His general approach to measure and dimension led to profound developments in numerous mathematical disciplines, and today Hausdorff dimension plays a central role in fractal theory with its many fascinating applications by means of computer graphics. Hausdorff s remarkable mathematical versatility is reflected in his published work: today, no fewer than thirteen concepts, theorems and procedures carry his name. Yet he was not only a creative mathematician Hausdorff was also an original philosophical thinker, a poet, essayist and man of letters. Under the pseudonym Paul Mongre, he published a volume of aphorisms, an epistemological study, a book of poetry, an oft-performed play, and a number of notable essays in leading literary journals. As a Jew, Felix Hausdorff was increasingly persecuted and humiliated under the National Socialist dictatorship. When deportation to a concentration camp was imminent, he, along with his wife and sister-in law, decided to take their own lives. This book will be of interest to historians and mathematicians already fascinated by the rich life of Felix Hausdorff, as well as to those readers who wish to immerse themselves in the intricate web of intellectual and political transformations during this pivotal period in European history.
Preface.- Notice for the Reader.- I. Family Background and Early
Intellectual Interests.- Hausdorffs Childhood and Youth.- Hausdorffs
Student Years and Short-lived Astronomical Career.- Hausdorffs Early
Mathematical Works.- II. A Double Life: the Mathematician Felix Hausdorff and
the Philosopher/Man of Letters Paul Mongre.- Paul Mongre as a Philosopher.-
Paul Mongre: Author, Essayist and Critic.- Mathematics takes First Priority.-
III. Hausdorffs Crowning Mathematical Works.- Hausdorff at the Pinnacle of
his Career.- Full Professor in Bonn, 19211933.- Hausdorffs Life during the
Nazi Dictatorship.- Bibliography.- Name Index.
Format: Hardback, 236 pages, height x width: 235x155 mm, 8 Illustrations, color; 15 Illustrations, black and white; X, 236 p. 23 illus., 8 illus. in color.
Series: Association for Women in Mathematics Series 33
Pub. Date: 24-Apr-2024
ISBN-13: 9783031516764
This is the fifth proceedings volume published under the Women in Numbers umbrella. The WIN workshops and their proceedings volumes are part of the WIN network, aimed at highlighting the research of women and gender minorities in number theory as well as increasing their participation and boosting their potential collaborations in number theory and related fields.
The volume contains research articles in the mathematical area of number theory, written by teams of scholars at all levels in the field. More information about the network, its goals and purpose, past and future conferences, and past proceedings volumes, can be found on the WIN website.
This volume contains research outcomes and results produced by the collaborative research groups created under the Women in Numbers V workshop, the 5th in its series. The actual workshop was to take place in 2020 at the Banff International Research Station in Banff, Canada, but could not take place onsite due to COVID. The associated research groups, each consisting of 1-2 leaders and 2-4 junior researchers, were formed nevertheless and their collaborations went ahead in purely virtual form, as well as other papers by author teams for which at least 50% of the authors identify as women or gender minorities. These contributions include original research and survey articles in a wide variety of subareas within number theory. The former present new cutting-edge research that will be of interest to experts in the field, to the benefit of their own research. The survey articles serve as an accessible introduction for graduate students and other readers to areas of number theory that may be outside their area of expertise.
From Fontaine-Mazur Conjecture to Analytic Pro-p-Groups: A Survey
(Abdellatif).- Orientations and Cycles in Supersingular Isogeny Graphs
(Stange).- Generalized Ramanujan-Sato Series Arising from Modular Forms
(Swisher).- Mock Theta Functions and Related Combinatorics
(Ballantine).- Transcendental Lattices of Certain Singular K3
Surfaces (Bertin).- Power-Saving Error Terms for the Number of D4-Quartic
Extensions over a Number Field Ordered by Discriminant (Lopez).- Dynamical
Mahler Measure: a Survey and Some Recent Results (Lalin).- Geometric
Decomposition of Abelian Varieties of Order 1 (Kedlaya).- On Marko Type
Surfaces over Number Fields and the Arithmetic of Marko Numbers
(Sivaraman).- p-Adic Measures for Reciprocals of L-Functions of Totally Real
Number Fields (Taha).
Format: Hardback, 211 pages, height x width: 235x155 mm, 5 Tables, color; 2 Illustrations, color; VII, 211 p. 2 illus. in color.
Series: Infosys Science Foundation Series
Pub. Date: 27-Apr-2024
ISBN-13: 9789819997497
This book features chapters written by renowned scientists from various parts of the world, providing an up-to-date survey of submanifold theory, spanning diverse topics and applications. The book covers a wide range of topics such as ChenRicci inequalities in differential geometry, optimal inequalities for Casorati curvatures in quaternion geometry, conformal -RicciYamabe solitons, submersion on statistical metallic structure, solitons in f(R, T)-gravity, metric-affine geometry, generalized Wintgen inequalities, tangent bundles, and Lagrangian submanifolds. Moreover, the book showcases the latest findings on Pythagorean submanifolds and submanifolds of four-dimensional f-manifolds. The chapters in this book delve into numerous problems and conjectures on submanifolds, providing valuable insights for scientists, educators, and graduate students looking to stay updated with the latest developments in the field. With its comprehensive coverage and detailed explanations, this book is an essential resource for anyone interested in submanifold theory.
PrefaceRecent Developments on ChenRicci Inequalities in Differential Geometry
Bang-Yen Chen and Adara M. Blaga
Solitons in F(R, T)-Gravity
U. C. De and Krishnendu De
A Survey on Lagrangian Submanifolds of Nearly Kaehler 6-Sphere
Ramesh Sharma
Pythagorean Submanifolds
Muhittin Evren Aydin, Adela Mihai and Cihan Ozgur
On 4-Dimensional Submanifolds of F-manifolds
Beldjlali Gherici
Almost Yamabe Solitons on a Total Space of Almost Hermitian Submersions
Tanveer Fatima, Mehmet Akif Akyol and Rakesh Kumar
Generalized Wintgen Inequalities for ()-Para Sasakian Manifold
Majid Ali Choudhary, Lovejoy S. Das, Mohd Danish Siddiqi and Oguz Bahadir
Certain Optimal Inequalities for Casorati Curvatures in Quaternion Geometry
Mohd. Danish Siddiqi, Aliya Naaz Siddiqui and Kamran Ahmad
Gravity and Dark Matter in the Framework of Metric-Affine Geometry
Ghodratallah Fasihi-Ramandi and Vahid Pirhadi
Submersion on Statistical Metallic Structure
Mohit Saxena
Tangent Bundles Endowed with Quarter-Symmetric Non-Metric -Connection on
3-Dimensional Quasi-Sasakian Manifolds
Mohammad Nazrul Islam Khan and Ljubica VelimiroviLc
The Darboux Mate and the Higher-Order Curvatures of Spherical Legendre
Curves
Mircea Crasmareanu
Conformal -RicciYamabe Solitons in the Framework of Riemannian Manifolds
Sudhakar Kumar Chaubey and Abdul Haseeb
Format: Hardback, 358 pages, height x width: 235x155 mm, 6 Illustrations, color; 4 Illustrations, black and white; XII, 358 p. 10 illus., 6 illus. in color.,
Series: Association for Women in Mathematics Series 32
Pub. Date: 18-May-2024
ISBN-13: 9783031521621
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.
ForewordPrefaceTable of Contents
On homomorphic encryption using abelian groups: Classical security
analysisEleni Agathocleous, Vishnupriya Anupindi, Annette Bachmayr, Chloe
Martindale, Rahinatou Yuh Njah Nchiwo and Mima Stanojkovski
A survey of local-global methods for Hilberts Tenth ProblemSylvy Anscombe,
Valentn Karemaker, Zeynep Kisakurek, Vler? Mehmeti, Margherita Pagano and
Laura Paladino
Sums of proper divisors with missing digitsKubra Benli, Giulia Cesana,
Cecile Dartyge, Charlotte Dombrowsky, and Lola Thompson
Rational approximations, multidimensional continued fractions and lattice
reductionV. BerthLe, K. Dajani, C. Kalle, E. Krawczyk, H. Kuru and A. Thevis
Campana points on diagonal hypersurfacesFrancesca Balestrieri, Julia Brandes,
Miriam Kaesberg, Judith Ortmann, Marta Pieropan, Rosa Winter
Power values of power sums: A surveyNirvana Coppola, Mar Curco-Iranzo,
Maleeha Khawaja, Vandita Patel and Ozge Ulkem
Transcendence measure of e^{1/n}Marta Dujella, Anne-Maria Ernvall-Hytonen,
Linda Frey and Bidisha Roy
Real quadratic singular moduli and p-adic families of modular formsPaulina
Fust, Judith Ludwig, Alice Pozzi, Mafalda Santos and Hanneke Wiersema
Elliptic fibrations and involutions on K3 surfacesAlice Garbagnati and
Cec?lia Salgado
Mirror constructions for K3 surfaces from bimodal singularitiesMakiko Mase
and Ursula Whitcher
Variants of the Li-type criteria for the Generalized Riemann hypothesisA.-M.
Ernvall-Hytonen, A. Odak, L. Smajlovic and M. Zubaca
A note on the non-vanishing of Poincare seriesSonja unar