Content deleted Content added
Citation bot (talk | contribs) Add: url, s2cid. | You can use this bot yourself. Report bugs here. | Suggested by SemperIocundus | via #UCB_webform |
m link [pP]ower series |
||
Line 4:
==Serre's definition==
Serre defined a ''p''-adic modular form to be a formal [[power series]] with ''p''-adic coefficients that is a ''p''-adic limit of classical modular forms with integer coefficients. The weights of these classical modular forms need not be the same; in fact, if they are then the ''p''-adic modular form is nothing more than a linear combination of classical modular forms. In general the weight of a ''p''-adic modular form is a ''p''-adic number, given by the limit of the weights of the classical modular forms (in fact a slight refinement gives a weight in '''Z'''<sub>''p''</sub>×'''Z'''/(''p''–1)'''Z''').
The ''p''-adic modular forms defined by Serre are special cases of those defined by Katz.
| |||