| Title:
|
The equidistribution of Fourier coefficients of half integral weight modular forms on the plane (English) |
| Author:
|
Mezroui, Soufiane |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
235-249 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $f=\sum _{n=1}^{\infty }a(n)q^{n}\in S_{k+1/2}(N,\chi _{0})$ be a nonzero cuspidal Hecke eigenform of weight $k+\frac {1}{2}$ and the trivial nebentypus $\chi _{0}$, where the Fourier coefficients $a(n)$ are real. Bruinier and Kohnen conjectured that the signs of $a(n)$ are equidistributed. This conjecture was proved to be true by Inam, Wiese and Arias-de-Reyna for the subfamilies $\{a(t n^{2})\}_{n}$, where $t$ is a squarefree integer such that $a(t)\neq 0$. Let $q$ and $d$ be natural numbers such that $(d,q)=1$. In this work, we show that $\{a(t n^{2})\}_{n}$ is equidistributed over any arithmetic progression $n\equiv d \mod q$. (English) |
| Keyword:
|
Shimura lift |
| Keyword:
|
Fourier coefficient |
| Keyword:
|
half-integral weight |
| Keyword:
|
Sato-Tate equidistribution |
| MSC:
|
11F30 |
| MSC:
|
11F37 |
| idZBL:
|
07217131 |
| idMR:
|
MR4078356 |
| DOI:
|
10.21136/CMJ.2019.0223-18 |
| . |
| Date available:
|
2020-03-10T10:18:52Z |
| Last updated:
|
2022-04-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148052 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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