Heegner points and derivatives ofL-series. II

Abstract. In this paper we obtain special value results for L-functions associated to classical and paramodular Saito-Kurokawa lifts. In particular, we consider standard L-functions associated to Saito-Kurokawa lifts as well as degree eight L-functions obtained by twisting with an automorphic form defined on GL(2). The results are obtained by combining classical and representation theoretic arguments.

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“…2.3, up to scaling this lift is unique. This allows us to apply Corollary 1 of [11] to conclude the following result. Lemma 4.3.…”

Section: Ratios Of Petersson Norms: the Level γmentioning

confidence: 83%

Special values of L-functions for Saito–Kurokawa lifts

Brown

Pitale

2013

Math. Proc. Camb. Phil. Soc.

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“…In this section, we present a modified way to get these lifts between J cusp k,m (M, χ) and S 2k−2 mM, χ 2 . The results of this section are straightforward applications of the known results [3,8,14], and so we omit the proofs.…”

Section: Preliminariesmentioning

confidence: 96%

“…, and where C Q is the image in Γ 0 (mM )\H of the semicircle a|w| 2 +bu+c = 0 (w = u+iv) with appropriate orientation (see [3,14] for details). Then …”

Section: The Holomorphic Kernel Function Of the Periods Of Cusp Formsmentioning

confidence: 99%

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On Shimura, Shintani and Eichler-Zagier correspondences

Manickam

Balasubramaniam

2000

Trans. Amer. Math. Soc.

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Abstract. In this paper, we set up Shimura and Shintani correspondences between Jacobi forms and modular forms of integral weight for arbitrary level and character, and generalize the Eichler-Zagier isomorphism between Jacobi forms and modular forms of half-integral weight to higher levels. Using this together with the known results, we get a strong multiplicity 1 theorem in certain cases for both Jacobi cusp newforms and half-integral weight cusp newforms. As a consequence, we get, among other results, the explicit Waldspurger theorem.

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“…Dorman [4] generalized this result to fundamental discriminants. Moreover, the contributions at the finite places to the height pairing studied in [5] essentially provide a generalization to higher level.…”

Section: Introductionmentioning

confidence: 99%

Singular moduli of higher level and special cycles

Ehlen

2015

Res Math Sci

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We describe the complex multiplication (CM) values of modular functions for Γ0(N ) whose divisor is given by a linear combination of Heegner divisors in terms of special cycles on the stack of CM elliptic curves. In particular, our results apply to Borcherds products of weight 0 for Γ0(N ). By working out explicit formulas for the special cycles, we obtain the prime ideal factorizations of such CM values.

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Heegner points and derivatives ofL-series. II

Cited by 281 publications

References 19 publications

Special values of L-functions for Saito–Kurokawa lifts

Special values of L-functions for Saito–Kurokawa lifts

On Shimura, Shintani and Eichler-Zagier correspondences

Singular moduli of higher level and special cycles

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