Automorphic Forms and Related Topics.
- 1st ed.
- 1 online resource (298 pages)
- Contemporary Mathematics Series ; v.732 .
- Contemporary Mathematics Series .
Cover -- Title page -- Contents -- Preface -- A note on the minimal level of realization for a mod ℓ eigenvalue system -- 1. Introduction and preliminaries -- 2. Notation and preliminaries on modular curves -- 3. Level lowering for Katz cuspforms -- 4. Proof of Theorem 1.3 -- Acknowledgments -- References -- A discussion on the number eta-quotients of prime level -- References -- Dedekind sums, reciprocity, and non-arithmetic groups -- 1. Dedekind sums -- 2. ...and modular transformations -- 3. Dedekind symbols -- 4. Equidistribution mod 1 -- 5. Reciprocity of Dedekind symbols -- References -- Noncommutative modular symbols and Eisenstein series -- 1. Introduction -- 2. Properties of iterated integrals -- 3. Eisenstein series twisted by noncommutative modular symbols -- 4. Meromorphic continuation -- 5. Higher-order automorphic forms and maps -- References -- An annotated discussion of a panel presentation on improving diversity in mathematics -- 1. Introduction -- 2. Issues of retention -- 3. Issues of recruitment -- 4. Conclusion -- References -- Superzeta functions, regularized products, and the Selberg zeta function on hyperbolic manifolds with cusps -- 1. Introduction -- 2. Zeta regularization of entire functions -- 3. Superzeta functions constructed from confinite Kleinian groups -- 4. Zeta regularization of zeta-type functions through integral representation -- 5. Superzeta functions constructed over non-trivial zeros of the Selberg zeta function on hyperbolic manifolds with cusps -- References -- Computing -adic periods of abelian varieties from automorphic forms -- 1. Introduction -- 2. Automorphic forms and abelian varieties -- 3. Periods of automorphic forms -- 4. Examples -- References -- An algebraic and analytic approach to spinor exceptional behavior in translated lattices -- References. Differential operators on Jacobi forms and special values of certain Dirichlet series -- 1. Introduction -- 2. Preliminaries on Jacobi forms of scalar index -- 3. Statement of the theorems -- 4. Proofs -- References -- Some results in study of Kronecker limit formula and Dedekind sums -- 1. Introduction -- 2. Generators of function fields for Atkin-Lehner groups -- 3. Elliptic Kronecker limit formula and a Weierstrass-type factorization theorem -- 4. Kronecker limit formula for higher order Eisenstein series and generalized Dedekind sums -- References -- Equidistribution of shears and their arithmetic applications -- 1. Introduction -- 2. The dynamical problem -- 3. Moments of ₂ automorphic -functions -- 4. Counting orbit points on affine quadrics -- References -- Fake proofs for identities involving products of Eisenstein series -- 1. Introduction -- 2. The identity in higher weight -- 3. An example related to Hecke operators -- References -- Modular forms constructed from moduli of elliptic curves, with applications to explicit models of modular curves -- 1. Lecture 1 -- 2. Lecture 2 -- 3. Exercises -- References -- Some remarks on the coefficients of symmetric power -functions -- 1. Introduction -- 2. Hoheisel phenomenon -- 3. Proof of Theorem 1.1 -- 4. Proof of Theorem 1.2 -- 5. Proof of Theorem 1.3 -- References -- On primes in arithmetic progressions -- References -- The Fourier coefficients of Eisenstein series newforms -- 1. Introduction -- 2. A newform theory for Eisenstein series -- 3. The strong multiplicity-one theorem and matching densities -- 4. Sign changes of Fourier coefficients -- Acknowledgments -- References -- Properties of Sturm's formula -- 1. Holomorphic projection -- 2. Poincaré series -- 3. Sturm's operator -- 4. Spectral point of view -- 5. Perspectives -- References. An application of a special form of a Tauberian theorem -- 1. Introduction -- 2. A Tauberian theorem with an optimal bound for the remainder term -- 3. The Weyl law -- References -- On the zeros of some functions from the extended Selberg class -- 1. Introduction -- 2. Certain families of functions with zeros in the half-plane \re > -- 1 -- 3. Numerical criterion for detecting half-planes containing zeros of function -- References -- Rational points on twisted modular curves -- 1. Introduction -- 2. Twists of ₀( ) -- 3. Violation of the Hasse Principle -- 4. Quadratic Points on Modular Curves -- 5. Further Questions -- References -- On the number of representations of certain quadratic forms in 8 variables -- 1. Introduction -- 2. Preliminaries and Statement of Results -- 3. Proofs -- Acknowledgments -- References -- Level of Siegel modular forms constructed via ³ lifting -- 1. Introduction -- 2. Current work -- References -- Dimension formulas and kernel functions for Hilbert modular forms -- 1. Introduction -- 2. Classical modular forms -- 3. Dimension formulas -- 4. Dimension formula for Hilbert modular forms -- References -- An explicit evaluation of the Hauptmoduli at elliptic points for certain arithmetic groups -- 1. Introduction -- 2. Main results -- 3. An example: =29 -- 4. Hauptmodul values at elliptic points -- 5. An example: =29 -- 6. Further evaluations -- Acknowledgments -- References -- Torsion groups of elliptic curves over quadratic fields -- References -- Maass space for lifting from SL(2,ℝ) to GL(2,B) over a division quaternion algebra -- 1. Introduction: -- 2. Current work: -- References -- On the occurrence of large positive Hecke eigenvalues for GL(2) -- 1. Introduction -- 2. Background -- 3. Proof -- References -- Representations by quadratic forms and the Eichler Commutation Relation -- References. Degenerate principal series and Langlands classification -- 1. Introduction -- Notation -- 2. Degenerate principal series representations and Weil representations -- 3. Main theorems -- 4. Jacquet modules of degenerate principal series representations -- 5. Proof of the main theorem -- 6. Degenerate principal series for general linear groups -- References -- Back Cover.
This volume contains the proceedings of the Building Bridges: 3rd EU/US Summer School and Workshop on Automorphic Forms and Related Topics, which was held in Sarajevo from July 11-22, 2016. The articles summarize material which was presented during the lectures and speed talks during the workshop.These articles address various aspects of the theory of automorphic forms and its relations with the theory of L-functions, the theory of elliptic curves, and representation theory.In addition to mathematical content, the workshop held a panel discussion on diversity and inclusion, which was chaired by a social scientist who has contributed to this volume as well.This volume is intended for researchers interested in expanding their own areas of focus, thus allowing them to "build bridges" to mathematical questions in other fields.