On twisting operators and newforms of half-integral weight

Ueda, Masaru

doi:10.1017/s002776300000458x

Cited by 22 publications

(92 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By using this relation, we can deduce properties of X p from those of Y p . In particular, from [Ul,Proposition (1.27)], we have the above relation (3).…”

Section: Proposition 4 Let P Be Any Prime Divisor Of MI and F Any Elmentioning

confidence: 92%

“…On the other hand, from [Ul,(3.10)] for the spaces S(k+ 1/2, N{μ)/p, rf ( 2 ))x an< i V{N{θί)/p] r) f (~))κ, the system of eigen values of g f corresponds to a primitive form of weight 2k and of a conductor prime to p. This is a contradiction. Hence we have θ p = <£p.…”

Section: U(a 2 )mentioning

confidence: 99%

“…We apply results of §1 to calculations of §2. In §2, we will complete an attempt in the previous paper [Ul,§4]. §3 is the main part of this paper.…”

Section: Complete Theory Of Newforms For Kohnen Space 121mentioning

confidence: 99%

“…In the case of weight 3/2, we deal only with this complement V (N χ). See [Ul,§0,§1] [ Q °) (mod 7V/Q).…”

mentioning

confidence: 99%

“…Put W(Q) := 7g *JQ E ®{k + 1/2). See [Ul,§1] for the details of properties of these δ m and W(Q). Let f(z) = Σ^= o a(ή) e(nz) E G(fc + 1/2, JV, χ) and ^ a primitive character modulo f(^).…”

mentioning

confidence: 99%

See 4 more Smart Citations

On twisting operators and newforms of half-integral weight II – Complete theory of newforms for Kohnen space

Ueda

1998

Nagoya Mathematical Journal

Self Cite

View full text Add to dashboard Cite

Abstract. The author continues his previous work with the purpose of establishing a theory of newforms in the case of half-integral weight. In this paper, the author formulates and proves a complete theory of newforms for Kohnen space. Kohnen space is an important canonical subspace in the space of cusp forms of half-integral weight k + 1/2 (k > 0). Every Hecke common eigenform in Kohnen space corresponds to a primitive form of integral weight 2k and of odd level via Shimura Correspondence.These newforms for Kohnen space satisfy the Strong multiplicity One theorem. Moreover, we explicitly determine the corresponding primitive form (of weight 2k) to each newform for Kohnen space. The space of oldforms is also explicitly described.In order to find all newforms for Kohnen space, the author needs a certain non-vanishing property of Fourier coefficients of cusp forms. Such property proves by using representation theory of finite linear groups. The method of proof of newform theory is mainly based on trace formulae and trace relations.

show abstract

“…By using this relation, we can deduce properties of X p from those of Y p . In particular, from [Ul,Proposition (1.27)], we have the above relation (3).…”

Section: Proposition 4 Let P Be Any Prime Divisor Of MI and F Any Elmentioning

confidence: 92%

Section: U(a 2 )mentioning

confidence: 99%

“…We apply results of §1 to calculations of §2. In §2, we will complete an attempt in the previous paper [Ul,§4]. §3 is the main part of this paper.…”

Section: Complete Theory Of Newforms For Kohnen Space 121mentioning

confidence: 99%

“…In the case of weight 3/2, we deal only with this complement V (N χ). See [Ul,§0,§1] [ Q °) (mod 7V/Q).…”

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

On twisting operators and newforms of half-integral weight II – Complete theory of newforms for Kohnen space

Ueda

1998

Nagoya Mathematical Journal

Self Cite

View full text Add to dashboard Cite

show abstract

On the Kohnen-Zagier formula in the case of level 4pm

Sakata

2005

Math. Z.

View full text Add to dashboard Cite

On newforms for Kohnen plus spaces

Ueda

Yamana

2008

Math. Z.

Self Cite

View full text Add to dashboard Cite

In this article, we investigate the plus space of level N , where 4 −1 N is a squarefree (not necessarily odd) integer. This is a generalization of Kohnen's work. We define a Hecke isomorphism ℘ k of M k+1/2 (4M) onto M + k+1/2 (8M) for any odd positive integer M. The methods of the proof of the newform theory are this isomorphism, Waldspurger's theorem, and the dimension identity.Keywords Forms of half-integral weight · Newforms · Shimura correspondence · Kohnen plus space Mathematics Subject Classification (2000) 11F37 IntroductionThe purpose of this paper is to establish the theory of newforms for the Kohnen plus space with respect to 0 (N ), where 4 −1 N is a square-free integer. This is a continuation of Kohnen's work (cf. [1]) in the case when 4 −1 N is odd square-free.Let us describe our results. The space of cusp forms of weight k + 1/2 with respect to 0 (N ) is denoted by S k+1/2 (N ) and the Kohnen plus space S + k+1/2 (N ) is defined by S. Yamana thanks Prof. Ikeda for useful discussion, and he is supported by JSPS Research Fellowships for Young Scientists.

show abstract

On twisting operators and newforms of half-integral weight

Cited by 22 publications

References 21 publications

On twisting operators and newforms of half-integral weight II – Complete theory of newforms for Kohnen space

On twisting operators and newforms of half-integral weight II – Complete theory of newforms for Kohnen space

On the Kohnen-Zagier formula in the case of level 4pm

On newforms for Kohnen plus spaces

Contact Info

Product

Resources

About