Rocky Mountain Journal of Mathematics

Note on Igusa's cusp form of weight 35

Toshiyuki Kikuta, Hirotaka Kodama, and Shoyu Nagaoka

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Abstract

A congruence relation satisfied by Igusa's cusp form of weight~35 is presented. As a tool to confirm the congruence relation, a Sturm-type theorem for the case of odd-weight Siegel modular forms of degree~2 is included.

Article information

Source
Rocky Mountain J. Math., Volume 45, Number 3 (2015), 963-972.

Dates
First available in Project Euclid: 21 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1440168298

Digital Object Identifier
doi:10.1216/RMJ-2015-45-3-963

Mathematical Reviews number (MathSciNet)
MR3385972

Zentralblatt MATH identifier
1368.11043

Subjects
Primary: 11F33: Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50]
Secondary: 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms

Citation

Kikuta, Toshiyuki; Kodama, Hirotaka; Nagaoka, Shoyu. Note on Igusa's cusp form of weight 35. Rocky Mountain J. Math. 45 (2015), no. 3, 963--972. doi:10.1216/RMJ-2015-45-3-963. https://projecteuclid.org/euclid.rmjm/1440168298


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References

  • H. Aoki and T. Ibukiyama, Simple graded rings of Siegel modular forms, differential operators and Borcherds products, Int. J. Math. 16 (2005), 249–279.
  • S. Böcherer, Über gewisse Siegelsche Modulformen zweiten Grades, Math. Ann. 261 (1982), 23-41.
  • S. Böcherer and S. Nagaoka, On mod $p$ properties of Siegel modular forms, Math. Ann. 338 (2007), 421–433.
  • D. Choi, Y. Choie and T. Kikuta, Sturm type theorem for Siegel modular forms of genus $2$ modulo $p$, Acta Arith. 158 (2013), 129–139.
  • J.-I. Igusa, On Siegel modular forms of genus two, Amer. J. Math. 84 (1962), 175–200; II, ibid. 86 (1964), 392–412.
  • ––––, On the ring of modular forms of degree two over $\boldsymbol{Z}$, Amer. J. Math. 101 (1979), 149–183.
  • C. Poor and D.S. Yuen, Paramodular cusp forms, arXiv:0912.0049v1 [math.NT], 1 Dec 2009.
  • J.-P. Serre, Formes modulaires et fonctions zêta $p$-adiques, Modular functions of one variable III, Lect. Notes Math. 350 (1972), 191–268.