A certain Dirichlet series of Rankin–Selberg type associated with the Ikeda lifting

Katsurada, Hidenori; Kawamura, Hisa-aki

doi:10.1016/j.jnt.2007.07.006

Cited by 10 publications

(11 citation statements)

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“…Indeed " F, G " on the page 2026, line 14 of [23] should read " 1 2 F, G " (cf. Krieg [29]) and therefore "2 2k−n+1 " on the page 2027, line 7 of [23] should read "2 2k−n ".…”

Section: (See the Remark Below) Thus Conjecture A Holds True If And mentioning

confidence: 99%

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

Katsurada

Kawamura

2015

Proc. London Math. Soc.

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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.

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“…Indeed " F, G " on the page 2026, line 14 of [23] should read " 1 2 F, G " (cf. Krieg [29]) and therefore "2 2k−n+1 " on the page 2027, line 7 of [23] should read "2 2k−n ".…”

Section: (See the Remark Below) Thus Conjecture A Holds True If And mentioning

confidence: 99%

“…Corollary to Proposition 3.1). Hence, by virtue of the main identity in [23], this enables us to rewrite Ikeda's conjecture in terms of the relation between the residue of R(s, σ n−1 (φ In(h),1 )) at s = k − 1/2 and the period of h (cf. Theorem 3.2).…”

Section: Introductionmentioning

confidence: 99%

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

Katsurada

Kawamura

2015

Proc. London Math. Soc.

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“…There the nonvanishing of the central value is important. Recently some progress has been obtained by Katsurada and Kawamura [KK06]. The focus of this paper is the proof of the arithmetic trace formula and not applications.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 97%

A Trace Formula of Special Values of Automorphic L-Functions

Heim

2012

Multiple Dirichlet Series, L-Functions and Automorphic Forms

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Abstract. Deligne introduced the concept of special values of automorphic L-functions. The arithmetic properties of these L-functions play a fundamental role in modern number theory. In this paper we prove a trace formula which relates special values of the Hecke, Rankin, and the central value of the Garrett triple L-function attached to primitive newforms. This type of trace formula is new and involves special values in the convergent and non-convergent domain of the underlying L-functions.

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“…In 2008, Katsurada and Kawamura [10, Main Theorem] proved following theorem which is crucial in the proof of our results. Theorem Let

n

and

k

be positive even integers such that

k > n + 1

.…”

Section: Notations and Preliminariesmentioning

confidence: 90%

Ramanujan–Petersson conjecture for Fourier–Jacobi coefficients of Siegel cusp forms

Kumar

Paul

2020

Bull. London Math. Soc.

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Let F be a Siegel cusp form of weight k and degree n>1 with Fourier‐Jacobi coefficients {ϕm}m∈N. In this article, we investigate the Ramanujan–Petersson conjecture (formulated by Kohnen) for the Petersson norm of ϕm. In particular, we show that this conjecture is true when F is a Hecke eigenform and a Duke–Imamoğlu–Ikeda lift. This generalizes a result of Kohnen and Sengupta. Further, we investigate an omega result and a lower bound for the Petersson norms of ϕm as m→∞. Interestingly, these results are different depending on whether F is a Saito–Kurokawa lift or a Duke–Imamoğlu–Ikeda lift of degree n⩾4.

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A certain Dirichlet series of Rankin–Selberg type associated with the Ikeda lifting

Cited by 10 publications

References 10 publications

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

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

A Trace Formula of Special Values of Automorphic L-Functions

Ramanujan–Petersson conjecture for Fourier–Jacobi coefficients of Siegel cusp forms

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