Shintani and Shimura lifts of cusp forms on certain arithmetic groups and their applications

• Autorzy: SoYoung Choi , Chang Heon Kim
• Języki publikacji: EN

Abstrakty

EN

For an odd and squarefree level N, Kohnen proved that there is a canonically defined subspace [...] S κ + 1 2 n e w ( N ) ⊂ S κ + 1 2 ( N ) , and S κ + 1 2 n e w ( N ) and S 2 k n e w ( N ) $S_{\kappa+\frac{1}{2}}^{\mathrm{n}\mathrm{e}\mathrm{w}}(N)\subset S_{\kappa+\frac{1}{2}}(N),\,\,{\text{and}}\,\,S_{\kappa+\frac{1}{2}}^{\mathrm{n}\mathrm{e}\mathrm{w}}(N)\,\,{\text{and}}\,\,S_{2k}^{\mathrm{n}\mathrm{e}\mathrm{w}}(N)$ are isomorphic as modules over the Hecke algebra. Later he gave a formula for the product [...] a g ( m ) a g ( n ) ¯ $a_{g}(m)\overline{a_{g}(n)}$ of two arbitrary Fourier coefficients of a Hecke eigenform g of halfintegral weight and of level 4N in terms of certain cycle integrals of the corresponding form f of integral weight. To this end he first constructed Shimura and Shintani lifts, and then combining these lifts with the multiplicity one theorem he deduced the formula in [2, Theorem 3]. In this paper we will prove that there is a Hecke equivariant isomorphism between the spaces [...] S 2 k + ( p ) and S k + 1 2 ( p ) . $S_{2k}^{+}(p)\,\,{\text{and}}\,\,\mathbb{S}_{k+\frac{1}{2}}(p).$ We will also construct Shintani and Shimura lifts for these spaces, and prove a result analogous to [2, Theorem 3].

Słowa kluczowe

EN

Modular forms; Shintani lifts; Shimura lifts

Kategorie tematyczne

• 11F67: Special values of automorphic L -series, periods of modular forms, cohomology, modular symbols
• 11F37: Forms of half-integer weight; nonholomorphic modular forms
• 11F11: Holomorphic modular forms of integral weight

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 304-316

Daty

wydano

2017-01-01

otrzymano

2016-08-02

zaakceptowano

2017-01-03

online

2017-03-30

Twórcy

autor

SoYoung Choi

• Department of Mathematics Education and RINS, Gyeongsang National University, 501 Jinjudae-ro, Jinju, 660-701,

autor

Chang Heon Kim

• Department of Mathematics, Sungkyunkwan University, Suwon, 440-746,

Identyfikatory

DOI

10.1515/math-2017-0020