On basis problem for Siegel modular forms of degree 2

Ozeki, Michio

doi:10.4064/aa-31-1-17-30

Cited by 11 publications

(12 citation statements)

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“…The reduced quadratic matrices of size four which are expressed in the form (4.1) are displayed as t 11 , t 22 , t 33 , t 44 , t 12 , t 13 , t 23 , a = t 14 , b = t 24 , c = t 34 .…”

Section: A Very Small Table Of the Fourier Coefficients Of The Squarementioning

confidence: 99%

A Numerical Study of Siegel Theta Series of Various Degrees for the 32-Dimensional Even Unimodular Extremal Lattices

Oura¹,

Ozeki

2016

Kyushu J. Math.

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Abstract. Erokhin showed that the Siegel theta series associated with the even unimodular 32-dimensional extremal lattices of degree up to three is unique. Later, Salvati Manni showed that the difference of the Siegel theta series of degree four associated with the two even unimodular 32-dimensional extremal lattices is a constant multiple of the square J 2 of the Schottky modular form J , which is a Siegel cusp form of degree four and weight eight. In the present paper we show that the Fourier coefficients of the Siegel theta series associated with the even unimodular 32-dimensional extremal lattices of degrees two and three can be computed explicitly, and the Fourier coefficients of the Siegel theta series of degree four for those lattices are computed almost explicitly.

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“…The reduced quadratic matrices of size four which are expressed in the form (4.1) are displayed as t 11 , t 22 , t 33 , t 44 , t 12 , t 13 , t 23 , a = t 14 , b = t 24 , c = t 34 .…”

Section: A Very Small Table Of the Fourier Coefficients Of The Squarementioning

confidence: 99%

A Numerical Study of Siegel Theta Series of Various Degrees for the 32-Dimensional Even Unimodular Extremal Lattices

Oura¹,

Ozeki

2016

Kyushu J. Math.

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“…In case N 1, it follows from [22] that .///'2(1) (4) is generated by 2(; L(d+)) for n 8, 24, 32, 40, and by 92(; L(#2g)). This proves surjectivity.…”

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confidence: 99%

“…[5], if (I, B) is a generator matrix for C, where B Mat.,_(F), and I is the k x k by guest onAugust 11, 2015 http://imrn.oxfordjournals.org/ Downloaded from…”

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confidence: 99%

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Duke¹

1993

Internat. Math. Res. Notices

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“…(1)- (1) (1)- (2) (2) When n = 3 and L = 1324 (see [5]), along the method of calculation developed in [5] we can calculate the Fourier coefficients oftheta-series of degree 3 attached to L. …”

Section: T=(' T2mentioning

confidence: 99%