**Contemporary Mathematics**

Volume: 732;
2019;
286 pp;
Softcover

MSC: Primary 11; 14; 22; 32;

**Print ISBN: 978-1-4704-3525-7
Product Code: CONM/732**

List Price: $117.00

AMS Member Price: $93.60

MAA Member Price: $105.30

**Electronic ISBN: 978-1-4704-5317-6
Product Code: CONM/732.E**

List Price: $117.00

AMS Member Price: $93.60

MAA Member Price: $105.30

# Automorphic Forms and Related Topics

Share this page *Edited by *
*Samuele Anni; Jay Jorgenson; Lejla Smajlović; Lynne Walling*

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.

#### Readership

Graduate students and research mathematicians interested in number theory, representation theory, and arithmetic geometry.

# Table of Contents

## Automorphic Forms and Related Topics

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- A note on the minimal level of realization for a mod ℓ eigenvalue system 110
- A discussion on the number eta-quotients of prime level 1524
- Dedekind sums, reciprocity, and non-arithmetic groups 1928
- Noncommutative modular symbols and Eisenstein series 2736
- An annotated discussion of a panel presentation on improving diversity in mathematics 4756
- Superzeta functions, regularized products, and the Selberg zeta function on hyperbolic manifolds with cusps 5766
- 1. Introduction 5766
- 2. Zeta regularization of entire functions 5968
- 3. Superzeta functions constructed from confinite Kleinian groups 6271
- 4. Zeta regularization of zeta-type functions through integral representation 6574
- 5. Superzeta functions constructed over non-trivial zeros of the Selberg zeta function on hyperbolic manifolds with cusps 6776
- References 7281

- Computing 𝑝-adic periods of abelian varieties from automorphic forms 7584
- An algebraic and analytic approach to spinor exceptional behavior in translated lattices 8594
- Differential operators on Jacobi forms and special values of certain Dirichlet series 91100
- Some results in study of Kronecker limit formula and Dedekind sums 101110
- Equidistribution of shears and their arithmetic applications 125134
- Fake proofs for identities involving products of Eisenstein series 133142
- Modular forms constructed from moduli of elliptic curves, with applications to explicit models of modular curves 139148
- Some remarks on the coefficients of symmetric power 𝐿-functions 155164
- On primes in arithmetic progressions 165174
- The Fourier coefficients of Eisenstein series newforms 169178
- Properties of Sturm’s formula 177186
- An application of a special form of a Tauberian theorem 187196
- On the zeros of some 𝐿 functions from the extended Selberg class 195204
- Rational points on twisted modular curves 207216
- On the number of representations of certain quadratic forms in 8 variables 215224
- Level of Siegel modular forms constructed via 𝑠𝑦𝑚³ lifting 225234
- Dimension formulas and kernel functions for Hilbert modular forms 229238
- An explicit evaluation of the Hauptmoduli at elliptic points for certain arithmetic groups 245254
- Torsion groups of elliptic curves over quadratic fields 253262
- Maass space for lifting from SL(2,ℝ) to GL(2,B) over a division quaternion algebra 257266
- On the occurrence of large positive Hecke eigenvalues for GL(2) 259268
- Representations by quadratic forms and the Eichler Commutation Relation 267276
- Degenerate principal series and Langlands classification 275284
- 1. Introduction 275284
- Notation 276285
- 2. Degenerate principal series representations and Weil representations 277286
- 3. Main theorems 279288
- 4. Jacquet modules of degenerate principal series representations 280289
- 5. Proof of the main theorem 281290
- 6. Degenerate principal series for general linear groups 284293
- References 285294

- Back Cover Back Cover1298