Share

Automorphic Forms and Mock Modular Forms in String Theory

2017
Download Automorphic Forms and Mock Modular Forms in String Theory PDF Online Free

Author :
Release : 2017
Genre :
Kind : eBook
Book Rating : 640/5 ( reviews)

GET EBOOK


Book Synopsis Automorphic Forms and Mock Modular Forms in String Theory by : Caner Nazaroglu

Download or read book Automorphic Forms and Mock Modular Forms in String Theory written by Caner Nazaroglu. This book was released on 2017. Available in PDF, EPUB and Kindle. Book excerpt: We study a variety of modular invariant objects in relation to string theory. First, we focus on Jacobi forms over generic rank lattices and Siegel forms that appear in N = 2, D = 4 compactifications of heterotic string with Wilson lines. Constraints from low energy spectrum and modularity are employed to deduce the relevant supersymmetric partition functions entirely. This procedure is applied on models that lead to Jacobi forms of index 3, 4, 5 as well as Jacobi forms over root lattices A2 and A3. These computations are then checked against an explicit orbifold model which can be Higgsed to the models under question. Models with a single Wilson line are then studied in detail with their relation to paramodular group Gammam as T-duality group made explicit. These results on the heterotic string side are then turned into predictions for geometric invariants using TypeII - Heterotic duality. Secondly, we study theta functions for indenite signature lattices of generic signature. Building on results in literature for signature (n-1,1) and (n-2,2) lattices, we work out the properties of generalized error functions which we call r-tuple error functions. We then use these functions to build such indenite theta functions and describe their modular completions.

String Theory, Geometry and (mock) Modular Forms

2014
Download String Theory, Geometry and (mock) Modular Forms PDF Online Free

Author :
Release : 2014
Genre :
Kind : eBook
Book Rating : /5 ( reviews)

GET EBOOK


Book Synopsis String Theory, Geometry and (mock) Modular Forms by : Sarah Harrison

Download or read book String Theory, Geometry and (mock) Modular Forms written by Sarah Harrison. This book was released on 2014. Available in PDF, EPUB and Kindle. Book excerpt: Monstrous moonshine (Conway and Norton, c. 1980) is a relation between the "monster", the largest of the sporadic finite simple groups, and the j-function, the unique holomorphic weight zero modular function under SL(2, Z) with a simple pole at the infinite cusp. Recently, string theory has been the impetus for the discovery of a host of similar such relations, connecting many smaller finite groups to mock modular forms, the recalcitrant cousins of the j-function. Here I discuss some of these mysterious new connections, and progress we have made in understanding them by studying string theory on K3 manifolds. This thesis is based on the papers [157], [153], and [127] written with Miranda Cheng, Xi Dong, John Duncan, Shamit Kachru, Natalie Paquette, and Timm Wrase. It should not be cited without also referencing those papers.

Modular and Automorphic Forms & Beyond

2021-10-12 Automorphic forms
Download Modular and Automorphic Forms & Beyond PDF Online Free

Author :
Release : 2021-10-12
Genre : Automorphic forms
Kind : eBook
Book Rating : 673/5 ( reviews)

GET EBOOK


Book Synopsis Modular and Automorphic Forms & Beyond by : Hossein Movasati

Download or read book Modular and Automorphic Forms & Beyond written by Hossein Movasati. This book was released on 2021-10-12. Available in PDF, EPUB and Kindle. Book excerpt: The guiding principle in this monograph is to develop a new theory of modular forms which encompasses most of the available theory of modular forms in the literature, such as those for congruence groups, Siegel and Hilbert modular forms, many types of automorphic forms on Hermitian symmetric domains, Calabi-Yau modular forms, with its examples such as Yukawa couplings and topological string partition functions, and even go beyond all these cases. Its main ingredient is the so-called 'Gauss-Manin connection in disguise'.

Automorphic Forms

2014-11-19 Mathematics
Download Automorphic Forms PDF Online Free

Author :
Release : 2014-11-19
Genre : Mathematics
Kind : eBook
Book Rating : 526/5 ( reviews)

GET EBOOK


Book Synopsis Automorphic Forms by : Bernhard Heim

Download or read book Automorphic Forms written by Bernhard Heim. This book was released on 2014-11-19. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume presents a collection of carefully refereed articles covering the latest advances in Automorphic Forms and Number Theory, that were primarily developed from presentations given at the 2012 “International Conference on Automorphic Forms and Number Theory,” held in Muscat, Sultanate of Oman. The present volume includes original research as well as some surveys and outlines of research altogether providing a contemporary snapshot on the latest activities in the field and covering the topics of: Borcherds products Congruences and Codes Jacobi forms Siegel and Hermitian modular forms Special values of L-series Recently, the Sultanate of Oman became a member of the International Mathematical Society. In view of this development, the conference provided the platform for scientific exchange and collaboration between scientists of different countries from all over the world. In particular, an opportunity was established for a close exchange between scientists and students of Germany, Oman, and Japan. The conference was hosted by the Sultan Qaboos University and the German University of Technology in Oman.

Automorphic Forms

2012-08-29 Mathematics
Download Automorphic Forms PDF Online Free

Author :
Release : 2012-08-29
Genre : Mathematics
Kind : eBook
Book Rating : 35X/5 ( reviews)

GET EBOOK


Book Synopsis Automorphic Forms by : Anton Deitmar

Download or read book Automorphic Forms written by Anton Deitmar. This book was released on 2012-08-29. Available in PDF, EPUB and Kindle. Book excerpt: Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem. This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essential aspects and restricting it to the 'base field' of rational numbers. Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic.

You may also like...