Period Functions for Maass Wave Forms and Cohomology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Period Functions for Maass Wave Forms and Cohomology write by R. Bruggeman. This book was released on 2015-08-21. Period Functions for Maass Wave Forms and Cohomology available in PDF, EPUB and Kindle. The authors construct explicit isomorphisms between spaces of Maass wave forms and cohomology groups for discrete cofinite groups Γ⊂PSL2(R). In the case that Γ is the modular group PSL2(Z) this gives a cohomological framework for the results in Period functions for Maass wave forms. I, of J. Lewis and D. Zagier in Ann. Math. 153 (2001), 191-258, where a bijection was given between cuspidal Maass forms and period functions. The authors introduce the concepts of mixed parabolic cohomology group and semi-analytic vectors in principal series representation. This enables them to describe cohomology groups isomorphic to spaces of Maass cusp forms, spaces spanned by residues of Eisenstein series, and spaces of all Γ-invariant eigenfunctions of the Laplace operator. For spaces of Maass cusp forms the authors also describe isomorphisms to parabolic cohomology groups with smooth coefficients and standard cohomology groups with distribution coefficients. They use the latter correspondence to relate the Petersson scalar product to the cup product in cohomology.
On the Theory of Maass Wave Forms
On the Theory of Maass Wave Forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On the Theory of Maass Wave Forms write by Tobias Mühlenbruch. This book was released on 2020-05-06. On the Theory of Maass Wave Forms available in PDF, EPUB and Kindle. This textbook provides a rigorous analytical treatment of the theory of Maass wave forms. Readers will find this unified presentation invaluable, as it treats Maass wave forms as the central area of interest. Subjects at the cutting edge of research are explored in depth, such as Maass wave forms of real weight and the cohomology attached to Maass wave forms and transfer operators. Because Maass wave forms are given a deep exploration, this book offers an indispensable resource for those entering the field. Early chapters present a brief introduction to the theory of classical modular forms, with an emphasis on objects and results necessary to fully understand later material. Chapters 4 and 5 contain the book’s main focus: L-functions and period functions associated with families of Maass wave forms. Other topics include Maass wave forms of real weight, Maass cusp forms, and weak harmonic Maass wave forms. Engaging exercises appear throughout the book, with solutions available online. On the Theory of Maass Wave Forms is ideal for graduate students and researchers entering the area. Readers in mathematical physics and other related disciplines will find this a useful reference as well. Knowledge of complex analysis, real analysis, and abstract algebra is required.
Holomorphic Automorphic Forms and Cohomology
Holomorphic Automorphic Forms and Cohomology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Holomorphic Automorphic Forms and Cohomology write by Roelof Bruggeman. This book was released on 2018-05-29. Holomorphic Automorphic Forms and Cohomology available in PDF, EPUB and Kindle.
Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume
Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume write by Roelof Bruggeman. This book was released on 2023-07-31. Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume available in PDF, EPUB and Kindle. View the abstract.
Modular Forms
Modular Forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Modular Forms write by Henri Cohen. This book was released on 2017-08-02. Modular Forms available in PDF, EPUB and Kindle. The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and “fun” subject in itself and abounds with an amazing number of surprising identities. This comprehensive textbook, which includes numerous exercises, aims to give a complete picture of the classical aspects of the subject, with an emphasis on explicit formulas. After a number of motivating examples such as elliptic functions and theta functions, the modular group, its subgroups, and general aspects of holomorphic and nonholomorphic modular forms are explained, with an emphasis on explicit examples. The heart of the book is the classical theory developed by Hecke and continued up to the Atkin–Lehner–Li theory of newforms and including the theory of Eisenstein series, Rankin–Selberg theory, and a more general theory of theta series including the Weil representation. The final chapter explores in some detail more general types of modular forms such as half-integral weight, Hilbert, Jacobi, Maass, and Siegel modular forms. Some “gems” of the book are an immediately implementable trace formula for Hecke operators, generalizations of Haberland's formulas for the computation of Petersson inner products, W. Li's little-known theorem on the diagonalization of the full space of modular forms, and explicit algorithms due to the second author for computing Maass forms. This book is essentially self-contained, the necessary tools such as gamma and Bessel functions, Bernoulli numbers, and so on being given in a separate chapter.
