Timeline for The correct determinant exponent of the weight $k$-operator for defining Hecke operators/adelizing modular forms
Current License: CC BY-SA 4.0
8 events
when toggle format | what | by | license | comment | |
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May 4, 2019 at 15:08 | vote | accept | D_S | ||
May 4, 2019 at 8:23 | answer | added | David Loeffler | timeline score: 15 | |
May 3, 2019 at 23:11 | comment | added | D_S | I wouldn't necessarily want scalar matrices to act trivially. Scalar multiples of Hecke operators are fine. I just want to be comfortable adelizing modular forms and Hecke operators in the cleanest way possible | |
May 3, 2019 at 22:33 | comment | added | paul garrett | As a diagnostic, perhaps also of what you're wanting to happen, do you want scalar matrices to act trivially, or by a power of determinant? And, by what power of det? For that matter, how much do you care about multiplying Hecke operators by scalars? The underlying effect is the same, whatever we do, ... | |
May 3, 2019 at 22:23 | comment | added | user35360 | It doesn't matter. There is usually a factor of some exponent of the determinant in the definition of Hecke operators, so this normalization varies from author to author depending on the definition of the slash operator and vice-versa. The total exponent after you include the normalization of the Hecke operator would probably be the same. | |
May 3, 2019 at 22:07 | comment | added | D_S | In Diamond and Shurman they define it this way in Chapter 5 in order to introduce the double coset operator and then Hecke operators. | |
May 3, 2019 at 22:04 | comment | added | paul garrett | The Bump "definition" is surely correct, and the other is a typo: for example, to make modular forms with trivial central character, the $k-1$ exponent will never succeed (maybe apart from $k=2$? in fact, was that the context for the Diamond-Shurman statement? It would still be a misleading way to write it, even if so...) You can also compare Shimura's. | |
May 3, 2019 at 22:01 | history | asked | D_S | CC BY-SA 4.0 |