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CONGRUENCES BETWEEN EXTREMAL MODULAR FORMS AND THETA SERIES OF SPECIAL TYPES MODULO POWERS OF 2 AND 3
被引：1
|作者：
Koike, Masao
[1
]
机构：
[1] Kyushu Univ, Grad Sch Math, Fukuoka 8128560, Japan
关键词：
theta series;
extremal modular forms formal power series;
integer sequences;
D O I：
10.2206/kyushujm.63.123
中图分类号：
O1 [数学];
学科分类号：
0701 ;
070101 ;
摘要：
Heninger, Rains and Sloane proved that the nth root of the theta series of any extremal even unimodular lattice in R-n has integer coefficients if n is of the form 2(i) 3(j) 5(k) (iota >= 3) Motivated by their discovery, we find the congruences between extremal modular forms and theta series of special types modulo powers of 2 and 3 This assertion enables us to prove that the 2nth root and the (3n/2)th root of the extremal modular form of weight n/2 have at least one non-integer coefficient
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页码：123 / 132
页数：10
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