CONGRUENCES BETWEEN EXTREMAL MODULAR FORMS AND THETA SERIES OF SPECIAL TYPES MODULO POWERS OF 2 AND 3

• KOIKE Masao

  Graduate School of Mathematics Kyushu University

Abstract

Heninger, Rains and Sloane proved that the nth root of the theta series of any extremal even unimodular lattice in Rⁿ has integer coefficients if n is of the form 2ⁱ3^j5^k(i ≥ 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.

Journal

• Kyushu Journal of Mathematics

  Kyushu Journal of Mathematics 63 (1), 123-132, 2009

  Faculty of Mathematics, Kyushu University

Keywords

• theta series
• extremal modular forms
• formal power series
• integer sequences

Details

• CRID: 1390282680204394752
• NII Article ID: 130000135274
• NII Book ID: AA10994346
• DOI: 10.2206/kyushujm.63.123
• ISSN: 18832032
• ISSN: 13406116
• Web Site: https://www.jstage.jst.go.jp/article/kyushujm/63/1/63_1_123/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed