Massive deformations of Maass forms and Jacobi forms

We define one-parameter "massive" deformations of Maass forms and Jacobi forms. This is inspired by descriptions of plane gravitational waves in string theory. Examples include massive Green's functions (that we write in terms of Kronecker-Eisenstein series) and massive modular graph functions.

[1]  K. Bringmann,et al.  Zagier-type dualities and lifting maps for harmonic Maass–Jacobi forms , 2010 .

[2]  Carlos R Mafra,et al.  Elliptic multiple zeta values and one-loop superstring amplitudes , 2014, 1412.5535.

[3]  Ameya Pitale Jacobi Maaß forms , 2009 .

[4]  A. Erdélyi,et al.  Tables of integral transforms , 1955 .

[5]  B. Pioline,et al.  Threshold corrections, generalised prepotentials and Eichler integrals , 2015, 1502.00007.

[6]  John Corcoran,et al.  String theory , 1974, Journal of Symbolic Logic.

[7]  Non-Abelian Born–Infeld action and type I–heterotic duality (II): Nonrenormalization theorems , 2002, hep-th/0209064.

[8]  P. Fleig,et al.  Eisenstein Series and Automorphic Representations , 2015, 1511.04265.

[9]  Modular Invariance of Strings on PP-Waves with RR-flux , 2002, hep-th/0206010.

[10]  Carl Ludwig Siegel,et al.  Lectures on advanced analytic number theory , 1961 .

[11]  C. Itzykson,et al.  Two-dimensional field theories close to criticality , 1987 .

[12]  Non-Abelian Born–Infeld action and Type I–heterotic duality (I): Heterotic F6 terms at two loops☆ , 2002, hep-th/0207026.

[13]  Stefan Sjörs,et al.  Towards the one-loop Kähler metric of Calabi-Yau orientifolds , 2014, 1407.0027.

[14]  Thermal amplitudes in DLCQ superstrings on pp-waves , 2002, hep-th/0209145.

[15]  M. Headrick A solution manual for Polchinski's "String Theory" , 2008, 0812.4408.

[16]  P. Stevenhagen,et al.  ELLIPTIC FUNCTIONS , 2022 .

[17]  E. D'hoker,et al.  Modular Graph Functions , 2015, 1512.06779.

[18]  J. Maldacena,et al.  Strings in flat space and pp waves from N = 4 Super Yang Mills , 2002 .

[19]  B R Greene,et al.  String theory. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[20]  Strings in flat space and pp waves from ${\cal N}=4$ Super Yang Mills , 2002, hep-th/0202021.

[21]  C. M. Linton,et al.  The Green's Function for the Two-Dimensional Helmholtz Equation in Periodic Domains , 1998 .

[22]  J. Polchinski An introduction to the bosonic string , 1998 .

[23]  N. Warner,et al.  Anomaly cancelling terms from the elliptic genus , 1988 .

[24]  R. Horgan,et al.  Statistical Field Theory , 2014 .

[25]  E. D'hoker,et al.  On the modular structure of the genus-one Type II superstring low energy expansion , 2015, 1502.06698.

[26]  R. Penrose Any Space-Time has a Plane Wave as a Limit , 1976 .