14
votes
Accepted
Why the level of a half integral weight modular form must be a multiple of 4?
The problem isn't that $S_{k + 1/2}(\Gamma_0(N))$ is zero if $4 \nmid N$; it's that the space is not defined if $4 \nmid N$.
In order to make sense of what a "half-integer weight form of level $\...
- 37k
8
votes
Accepted
(Explicit) Basis for Kohnen's plus-space of modular forms of half integral weight
There does exist an explicit basis when $k$ is EVEN: denote by
$E_{k,4}$ the Eisenstein series $E_k(4\tau)$. Then the Rankin-Cohen
brackets $[\theta,E_{k-2j,4}]_j$ for $0\le j\le\lfloor k/6\rfloor$ (...
- 13.1k
7
votes
Accepted
Twisted modular forms of half-integral weight
In general, the statement is something like the following. (The following is Proposition 3.12 from Ken Ono's book "The Web of Modularity")
Suppose that $g(z) = \sum c(n) q^{n}$ is a half-integer ...
- 20.4k
4
votes
Accepted
Necessity of conditions $N$ odd, square-free and $\chi$ quadratic in Kohnen's plus space - modular forms of half-integral weight
This is not an answer and I cannot comment due to lack of reputation, but it seems to first pop up in his Lemma 4 on p. 50. This occurs after a long, very technical discussion about double coset ...
- 26
3
votes
Off critical line zeros for half integer weight $L$-functions
The following paper (page 6) discuss some examples of half-integral weight $L$-functions which has zeros not necessarily on the critical line.
https://arxiv.org/pdf/math/9411213.pdf
It is published ...
1
vote
Half integral weight modular forms that reduce to a nonzero constant modulo a given prime
If such a form does exist, then its level must be a multiple of $p$.
If $f = \sum a_{n} q^{n}$ is a half-integer weight modular form with integer coefficients with $a_{i} \equiv 0 \pmod{p}$ for all $...
- 20.4k
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