Springer Monographs in Mathematics

1989

DOI: 10.1007/3-540-29593-3

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Modular Forms

Toshitsune Miyake¹

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Counting the Number Of Orbits On K31

Smoothness Of Eigencurve At Critical Weight 2 Eisenstein Series1

Representations Numbers and Heegner Divisors1

Examples1

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Cited by 455 publications

(430 citation statements)

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“…where 14) and ζ N = exp( 2πi N ). From now on, we introduce a subscript "t" such as n t , which corresponds to the trivial flux v = 0.…”

Section: Counting the Number Of Orbits On K3mentioning

confidence: 99%

An Approach to Script N = 4 ADE Gauge Theory onK3

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2002

J. High Energy Phys.

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We propose a recipe for determination of the partition function of N = 4 ADE gauge theory on K3 by generalizing our previous results of the SU (N ) case. The resulting partition function satisfies Montonen-Olive duality for ADE gauge group.

“…where 14) and ζ N = exp( 2πi N ). From now on, we introduce a subscript "t" such as n t , which corresponds to the trivial flux v = 0.…”

Section: Counting the Number Of Orbits On K3mentioning

confidence: 99%

An Approach to Script N = 4 ADE Gauge Theory onK3

¹

,

²

2002

J. High Energy Phys.

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We propose a recipe for determination of the partition function of N = 4 ADE gauge theory on K3 by generalizing our previous results of the SU (N ) case. The resulting partition function satisfies Montonen-Olive duality for ADE gauge group.

“…Except when k = 2 and χ = ψ = 1, for all positive integer t, the power series [14], [19]). Note that, for any prime p,…”

Section: Smoothness Of Eigencurve At Critical Weight 2 Eisenstein Seriesmentioning

confidence: 99%

Geometry of the eigencurve at critical Eisenstein series of weight 2

2015

J. Théor. Nombres Bordeaux

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In this paper we show that the critical Eisenstein series of weight 2, E critp 2, is smooth in the eigencurve C(l), where l is a prime. We also show that E critp,ord l 2 is smooth in the full eigencurve C f ull (l) and E critp,ord l 1 ,ord l 2 2 is non-smooth in the full eigencurve C f ull (l 1 l 2 ). Further, we show that, E critp 2, is étale over the weight space in the eigencurve C(l). As a consequence, we show that level lowering conjecture of Paulin fails to hold at E critp,ord l 2 is étale over the weight space in C(ℓ) 9

“…Let Ω 0 = 1 2π y −2 dx ∧ dy be the differential form on X D 0 (N), then from [KRY,(2.7)] and [Mi,Lemma 5.3.2] we know…”

Section: Representations Numbers and Heegner Divisorsmentioning

confidence: 99%

Ternary quadratic forms and Heegner divisors

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2015

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Abstract. In this paper, I use Siegel-Weil formula and Kudla matching principle to prove some interesting identities between representation number (of ternary quadratic space ) and the degree of Heegner divisors.

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