Modular Forms and Fourier Expansion

被引：0
|
作者：
Horinaga, Shuji [1 ]
机构：
[1] NTT Institute for Fundamental Mathematics, NTT Communication Science Laboratories
来源：
NTT Technical Review | 2024年 / 22卷 / 09期
关键词：
Fourier analysis; modular forms; representation theory;
D O I：
10.53829/ntr202409fa7
中图分类号：
学科分类号：
摘要：
Fourier analysis is an indispensable technology, but so is mathematics. In this article, we review the history of modular forms and give an overview of the relationship among representation theory, Fourier analysis, and modular forms. The explanation of difficult terms is confined to footnotes, and we focus on the relationship between the concepts. Finally, we discuss the remaining difficulties in the modern theory of modular forms, challenges, and the author’s research. © 2024 Nippon Telegraph and Telephone Corp.. All rights reserved.
引用
收藏
页码：59 / 64
页数：5
相关论文
共 50 条
  • [31] Congruence restricted modular forms
    Ludwick, K
    RAMANUJAN JOURNAL, 2005, 9 (03) : 341 - 356
  • [32] Integrable Lagrangians and modular forms
    Ferapontov, E. V.
    Odesskii, A. V.
    JOURNAL OF GEOMETRY AND PHYSICS, 2010, 60 (6-8) : 896 - 906
  • [33] Congruences between modular forms
    Thorne, Jack A.
    PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2024, 134 (01):
  • [34] Counting curves with modular forms
    Henningson, M
    Moore, G
    NUCLEAR PHYSICS B, 1996, 472 (03) : 518 - 528
  • [35] Crossing Probabilities and Modular Forms
    Peter Kleban
    Don Zagier
    Journal of Statistical Physics, 2003, 113 : 431 - 454
  • [36] Modular forms in Pari/GP
    Belabas, Karim
    Cohen, Henri
    RESEARCH IN THE MATHEMATICAL SCIENCES, 2018, 5
  • [37] Perspectives on mock modular forms
    Folsom, Amanda
    JOURNAL OF NUMBER THEORY, 2017, 176 : 500 - 540
  • [38] CONGRUENCES VIA MODULAR FORMS
    Osburn, Robert
    Sahu, Brundaban
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 139 (07) : 2375 - 2381
  • [39] On the critical points of modular forms
    Saber, Hicham
    Sebbar, Abdellah
    JOURNAL OF NUMBER THEORY, 2012, 132 (08) : 1780 - 1787
  • [40] The Burkhardt Group and Modular Forms
    Eberhard Freitag
    Riccardo Salvati Manni
    Transformation Groups, 2004, 9 : 25 - 45
12345