### Abstract

We study the traces of Hecke operators acting on the space of Jacobi forms and give the trace formula in the case of general odd squarefree level N by using results of Skoruppa and Zagier. As an application, we obtain some trace relations of them, and construct an isomorphism map from the space of all Jacobi cusp new forms of level N and index 1 having the eigenvalue +1 with respect to any Atkin-Lehner operator on the level to the space of all Jacobi cusp new forms of level 1 and index N whose eigenvalue with respect to any Atkin-Lehner operator on the index is equal to +1.

Original language | English |
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Journal | Journal of Number Theory |

DOIs | |

Publication status | Accepted/In press - 2017 |

### Fingerprint

### Keywords

- Jacobi forms
- Modular correspondences
- Trace formula

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

**Trace formula for Jacobi forms of odd squarefree level.** / Sakata, Hiroshi.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Trace formula for Jacobi forms of odd squarefree level

AU - Sakata, Hiroshi

PY - 2017

Y1 - 2017

N2 - We study the traces of Hecke operators acting on the space of Jacobi forms and give the trace formula in the case of general odd squarefree level N by using results of Skoruppa and Zagier. As an application, we obtain some trace relations of them, and construct an isomorphism map from the space of all Jacobi cusp new forms of level N and index 1 having the eigenvalue +1 with respect to any Atkin-Lehner operator on the level to the space of all Jacobi cusp new forms of level 1 and index N whose eigenvalue with respect to any Atkin-Lehner operator on the index is equal to +1.

AB - We study the traces of Hecke operators acting on the space of Jacobi forms and give the trace formula in the case of general odd squarefree level N by using results of Skoruppa and Zagier. As an application, we obtain some trace relations of them, and construct an isomorphism map from the space of all Jacobi cusp new forms of level N and index 1 having the eigenvalue +1 with respect to any Atkin-Lehner operator on the level to the space of all Jacobi cusp new forms of level 1 and index N whose eigenvalue with respect to any Atkin-Lehner operator on the index is equal to +1.

KW - Jacobi forms

KW - Modular correspondences

KW - Trace formula

UR - http://www.scopus.com/inward/record.url?scp=85028512532&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028512532&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2017.05.010

DO - 10.1016/j.jnt.2017.05.010

M3 - Article

AN - SCOPUS:85028512532

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -