Modular Forms are Everywhere: Celebration of Don Zagier’s 65th Birthday

This is a Topical Collection on Modular Forms, in honor of Don Zagier’s 65th Birthday.

Journal

Research in the Mathematical Sciences

Research in the Mathematical Sciences is an international, peer-reviewed journal encompassing the full scope of theoretical and applied mathematics, as well as theoretical computer...

Ken Ono

University of Virginia, USA
Kathrin Bringmann

University of Cologne, Germany
Maxim Kontsevich

Institut des Hautes Études Scientifiques, France
Pieter Moree

Max Planck Institute for Mathematics, Germany
Martin Westerholt-Raum

Chalmers Technical University, Sweden

Showing 1-25 of 25 articles

Modular forms are everywhere: celebration of Don Zagier’s 65th birthday
Ken Ono
Editorial 02 January 2019 Article: 15
A meromorphic extension of the 3D index
Stavros Garoufalidis
Rinat Kashaev
Research Open access 03 December 2018 Article: 8
Maass wave forms, quantum modular forms and Hecke operators
Seewoo Lee
Research 26 November 2018 Article: 7
Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis
John Lewis
Don Zagier
Research Open access 15 November 2018 Article: 4
Black holes and class groups
Nathan Benjamin
Shamit Kachru
Larry Rolen
Research 24 October 2018 Article: 43
A study of elliptic gamma function and allies
Vicenţiu Paşol
Wadim Zudilin
Research Open access 28 September 2018 Article: 39
Goursat rigid local systems of rank four
Danylo Radchenko
Fernando Rodriguez Villegas
Research Open access 05 September 2018 Article: 38
Modular forms in Pari/GP
Karim Belabas
Henri Cohen
Research 22 August 2018 Article: 37
A class of non-holomorphic modular forms III: real analytic cusp forms for \(\mathrm {SL}_2(\mathbb {Z})\)
Francis Brown
Research Open access 13 August 2018 Article: 34
Vector-valued Hirzebruch–Zagier series and class number sums
Brandon Williams
Research 07 May 2018 Article: 25
Modularity of generating series of winding numbers
Jan H. Bruinier
Jens Funke
Yingkun Li
Research 30 April 2018 Article: 23
Kronecker’s first limit formula, revisited
W. Duke
Ö. Imamoḡlu
Á. Tóth
Research 02 April 2018 Article: 20
Conjectures on correspondence of symplectic modular forms of middle parahoric type and Ihara lifts
Tomoyoshi Ibukiyama
Research 21 March 2018 Article: 18
Super-positivity of a family of L-functions in the level aspect
Dorian Goldfeld
Bingrong Huang
Research 13 March 2018 Article: 16
Taylor coefficients of non-holomorphic Jacobi forms and applications
Kathrin Bringmann
Research 23 February 2018 Article: 15
Quantum knot invariants
Stavros Garoufalidis
Research 08 February 2018 Article: 11
On the Colmez conjecture for non-abelian CM fields
Adrian Barquero-Sanchez
Riad Masri
Research 08 February 2018 Article: 10
A class of non-holomorphic modular forms I
Francis Brown
Research Open access 06 February 2018 Article: 7
Period polynomials, derivatives of L-functions, and zeros of polynomials
Nikolaos Diamantis
Larry Rolen
Research Open access 06 February 2018 Article: 9
Nonzero coefficients of half-integral weight modular forms mod \(\ell \)
Joël Bellaïche
Ben Green
Kannan Soundararajan
Research 31 January 2018 Article: 6
Holomorphic modular forms and cocycles
Roelof Bruggeman
Research Open access 30 January 2018 Article: 5
On Hecke’s decomposition of the regular differentials on the modular curve of prime level
Benedict H. Gross
Research 22 January 2018 Article: 1
Modular forms of real weights and generalised Dedekind symbols
Yuri I. Manin
Research Open access 22 January 2018 Article: 2
On the trace formula for Hecke operators on congruence subgroups, II
Alexandru A. Popa
Research 22 January 2018 Article: 3
Special values of motivic L-functions and zeta-polynomials for symmetric powers of elliptic curves
Steffen Löbrich
Wenjun Ma
Jesse Thorner
Research Open access 05 December 2017 Article: 26

Modular Forms are Everywhere: Celebration of Don Zagier’s 65th Birthday

Participating journal

Research in the Mathematical Sciences

Editors

Ken Ono

Kathrin Bringmann

Maxim Kontsevich

Pieter Moree

Martin Westerholt-Raum

Articles

Modular forms are everywhere: celebration of Don Zagier’s 65th birthday

A meromorphic extension of the 3D index

Maass wave forms, quantum modular forms and Hecke operators

Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis

Black holes and class groups

A study of elliptic gamma function and allies

Goursat rigid local systems of rank four

Modular forms in Pari/GP

A class of non-holomorphic modular forms III: real analytic cusp forms for \(\mathrm {SL}_2(\mathbb {Z})\)

Vector-valued Hirzebruch–Zagier series and class number sums

Modularity of generating series of winding numbers

Kronecker’s first limit formula, revisited

Conjectures on correspondence of symplectic modular forms of middle parahoric type and Ihara lifts

Super-positivity of a family of L-functions in the level aspect

Taylor coefficients of non-holomorphic Jacobi forms and applications

Quantum knot invariants

On the Colmez conjecture for non-abelian CM fields

A class of non-holomorphic modular forms I

Period polynomials, derivatives of L-functions, and zeros of polynomials

Nonzero coefficients of half-integral weight modular forms mod \(\ell \)

Holomorphic modular forms and cocycles

On Hecke’s decomposition of the regular differentials on the modular curve of prime level

Modular forms of real weights and generalised Dedekind symbols

On the trace formula for Hecke operators on congruence subgroups, II

Special values of motivic L-functions and zeta-polynomials for symmetric powers of elliptic curves

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Modular Forms are Everywhere: Celebration of Don Zagier’s 65th Birthday

Participating journal

Editors

Ken Ono

Kathrin Bringmann

Maxim Kontsevich

Pieter Moree

Martin Westerholt-Raum

Articles

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