Jacobi Eisenstein series over number fields

Boylan H.

JOURNAL OF NUMBER THEORY, cilt.248, ss.54-77, 2023 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 248
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1016/j.jnt.2023.01.007
  • Dergi Adı: JOURNAL OF NUMBER THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.54-77
  • İstanbul Üniversitesi Adresli: Evet

Özet

For any given totally real number field K, we compute the

Fourier developments of the Jacobi Eisenstein series over K

at the cusp at infinity. As main application we prove, for

any K with class number 1, that the L-series of the Jacobi

Eisenstein series of weight k ≥ 3 for indices with rank and

modified level 1 coincide with the L-series of the Eisenstein

series of weight 2k −2 on the full Hilbert modular group of K.

Moreover, under this correspondence the Fourier coefficients

of the Jacobi Eisenstein series are related to the twisted L-

series of the Hilbert Eisenstein series at the critical point by

a Waldspurger type identity. This is a first step in the proof

that Skoruppa’s and Zagier’s lifting from Jacobi forms over

Q to elliptic modular forms holds true over arbitrary totally

real number fields too.