Koecher–Maass series of a certain half-integral weight modular form related to the Duke–Imamoḡlu–Ikeda lift

Katsurada, Hidenori; Kawamura, Hisa-aki

doi:10.4064/aa162-1-1

Search citation statements

Order By: Relevance

Paper Sections

Select...

Now For An Element T ∈ L1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2015

Publication Types

Select...

Article1

Relationship

Self Cite1

Independent0

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This type of formal power series appears in an explicit formula of the Koecher-Maaß series associated with the Siegel Eisenstein series and the Duke-Imamoḡlu-Ikeda lift (cf. [11], [12], [25]). Therefore we say that this formal power series is of Koecher-Maaß type.…”

Section: Now For An Element T ∈ Lmentioning

confidence: 99%

Ikeda's conjecture on the period of the Duke–Imamoḡlu–Ikeda lift

Katsurada

Kawamura

2015

Proc. London Math. Soc.

Self Cite

View full text Add to dashboard Cite

Let k and n be positive even integers. For a cuspidal Hecke eigenform h in the Kohnen plus space of weight k − n/2 + 1/2 for Γ0(4), let In(h) be the Duke-Imamoḡlu-Ikeda lift of h in the space of cusp forms of weight k for Sp n (Z), and f be the primitive form of weight 2k − n for SL2(Z) corresponding to h under the Shimura correspondence. We then express the ratio In(h), In(h) / h, h of the period of In(h) to that of h in terms of special values of certain L-functions of f . This proves the conjecture proposed by Ikeda concerning the period of the Duke-Imamoḡlu-Ikeda lift.be the character corresponding to Q( √ D)/Q. Here we make the convention that D * = 1 if D = 1.

show abstract

Section: Now For An Element T ∈ Lmentioning

confidence: 99%