On Hermitian modular forms mod p

Toshiyuki Kikuta, Shōyū Nagaoka

Type: Article

Publication Date: 2011-01-01

Citations: 13

DOI: https://doi.org/10.2969/jmsj/06310211

Abstract

We generalize the notion of modular forms mod p to the case of Hermitian modular forms. Moreover we determine the structure of the algebra of degree 2 Hermitian modular forms mod p in the cases that the corresponding quadratic field is Q($\sqrt{-1}$) and Q($\sqrt{-3}$).

Locations

Journal of the Mathematical Society of Japan - View - PDF

Similar Works

Action	Title	Year	Authors
+	Structure of Hermitian modular forms modulo p and some applications	2021	Jaban Meher Sujeet Kumar Singh
+	On Hermitian theta series and modular forms	2009	Michael Hentschel Aloys Krieg
+	On symmetric hilbert modular forms	1996	Bernhard Runge
+	On modular representations of $$(\bar Q/Q)$$ arising from modular forms	1990	Kenneth A. Ribet
+	On p-divisibility of Fourier coefficients of Hermitian modular forms	2024	Shōyū Nagaoka
+	On the theta operator for Hermitian modular forms of degree 2	2016	Toshiyuki Kikuta Shōyū Nagaoka
+ PDF Chat	On the weights of mod p Hilbert modular forms	2010	Toby Gee
+	A Note on Hermitian Forms Over Fields of Characteristic 2	1964	Chih-Han Sah
+	Hermitian modular forms and the Burkhardt quartic	2005	Eberhard Freitag Riccardo Salvati Manni
+ PDF Chat	On quadratic, Hermitian and bilinear forms	1906	L. E. Dickson
+ PDF Chat	On Quadratic, Hermitian and Bilinear Forms	1906	L. E. Dickson
+	Modular quadratic and Hermitian forms over Dedekind rings.	1976	Colin J. Bushnell
+	Hermitian Modular Functions	1949	Hel Braun
+ PDF Chat	A note on modular forms $\mathrm{mod} p$	1979	Masao Koike
+	Differential operators on modular forms mod p	2019	Alexandru Ghitza
+	On p-divisibility of Fourier coefficients of Hermitian modular forms	2023	Shōyū Nagaoka
+	Differential operators on modular forms (mod p)	2018	Alexandru Ghitza
+	Differential operators on modular forms (mod p)	2018	Alexandru Ghitza
+	On quantum modular forms of non-zero weights	2022	Sandro Bettin Sary Drappeau
+	A Note on Modular Forms(MOD P)	1998	一幸畑田

Works That Cite This (13)

Action	Title	Year	Authors
+ PDF Chat	Congruences for Hermitian modular forms of degree 2	2011	Toshiyuki Kikuta
+ PDF Chat	Congruences in Hermitian Jacobi and Hermitian modular forms	2019	Jaban Meher Sujeet Kumar Singh
+	Differential operators for Hermitian Jacobi forms and Hermitian modular forms	2016	James D. Martin Jayantha Senadheera
+	On the theta operator for Hermitian modular forms of degree 2	2016	Toshiyuki Kikuta Shōyū Nagaoka
+ PDF Chat	A ring of symmetric Hermitian modular forms of degree 2 with integral Fourier coefficients	2019	Toshiyuki Kikuta
+	Note on mod p property of Hermitian modular forms	2016	Toshiyuki Kikuta Shōyū Nagaoka
+	Ramanujan type congruences for modular forms of several variables	2012	Toshiyuki Kikuta Shōyū Nagaoka
+	A ring of symmetric Hermitian modular forms of degree $2$ with integral Fourier coefficients	2019	Toshiyuki Kikuta
+ PDF Chat	Ramanujan type congruences for modular forms of several variables	2013	Toshiyuki Kikuta Shōyū Nagaoka
+	Structure of Hermitian modular forms modulo p and some applications	2021	Jaban Meher Sujeet Kumar Singh

Works Cited by This (9)

Action	Title	Year	Authors
+	On mod p properties of Siegel modular forms	2007	Siegfried Böcherer Shōyū Nagaoka
+	Graded rings of Hermitian modular forms of degree 2	2003	Tobias Dern Aloys Krieg
+	Note on mod p Siegel modular forms II	2005	Shōyū Nagaoka
+	The Maa� spaces on the Hermitian half-space of degree 2	1991	Aloys Krieg
+	Congruence properties of Hermitian modular forms	2008	Toshiyuki Kikuta Shōyū Nagaoka
+ PDF Chat	Hermitian modular forms congruent to 1 modulo p	2009	Michael Hentschel Gabriele Nebe
+	Formes modulaires et fonctions zêta p-adiques	2009	Jean-Pierre Serre
+	On Siegel Modular Forms of Genus Two	1962	Jun-ichi Igusa
+	On ℓ-ADIC Representations and Congruences for Coefficients of Modular Forms	2009	H. P. F. Swinnerton-Dyer