The Primary Role of Modular Equations

Harvey Cohn ()
Additional contact information
Harvey Cohn: City College (CUNY), Department o Mathematics

Chapter 3 in Number Theory: New York Seminar 1991–1995, 1996, pp 19-41 from Springer

Abstract: Abstract Recent developments indicate that the modular equation, historically the end product of modular function theory, should be considered as a starting point. For instance, while a Fourier series for a modular function has coefficients which determine a modular equation, conversely, modular functions are also determined by a modular equation. It is therefore of interest to ask what are the a priori determining features of a modular equation. Some features are revealed for the classic (one variable) case relating to normality of the parametrization. Other features are revealed for the Hilbert (two variable) case relating to the diagonals. A complete answer is still elusive, but a reasonable goal would be to find singular moduli directly (without modular invariants).

Keywords: Klein and Hecke modular functions; modular equations; Hilbert modular equations (search for similar items in EconPapers)
Date: 1996
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2418-1_3

Ordering information: This item can be ordered from
http://www.springer.com/9781461224181

DOI: 10.1007/978-1-4612-2418-1_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().