| Title:
|
Sign changes of certain arithmetical function at prime powers (English) |
| Author:
|
Agnihotri, Rishabh |
| Author:
|
Chakraborty, Kalyan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
4 |
| Year:
|
2021 |
| Pages:
|
1221-1228 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We examine an arithmetical function defined by recursion relations on the sequence $ \{f(p^k)\}_{k\in \mathbb {N}}$ and obtain sufficient condition(s) for the sequence to change sign infinitely often. As an application we give criteria for infinitely many sign changes of Chebyshev polynomials and that of sequence formed by the Fourier coefficients of a cusp form. (English) |
| Keyword:
|
arithmetic function |
| Keyword:
|
Dirichlet series |
| Keyword:
|
Chebyschev polynomial |
| Keyword:
|
modular form |
| MSC:
|
11A25 |
| MSC:
|
11B39 |
| MSC:
|
11F30 |
| MSC:
|
11M38 |
| idZBL:
|
Zbl 07442487 |
| idMR:
|
MR4339124 |
| DOI:
|
10.21136/CMJ.2021.0398-20 |
| . |
| Date available:
|
2021-11-08T16:07:35Z |
| Last updated:
|
2024-01-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149251 |
| . |
| Reference:
|
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| Reference:
|
[2] Banerjee, S.: A note on signs of Fourier coefficients of two cusp forms.Proc. Indian Acad. Sci., Math. Sci. 128 (2018), Article ID 43, 6 pages. Zbl 1448.11087, MR 3832998, 10.1007/s12044-018-0420-5 |
| Reference:
|
[3] Gun, S., Kohnen, W., Rath, P.: Simultaneous sign change of Fourier-coefficients of two cusp forms.Arch. Math. 105 (2015), 413-424. Zbl 1339.11055, MR 3413916, 10.1007/s00013-015-0829-3 |
| Reference:
|
[4] Knopp, M., Kohnen, W., Pribitkin, W.: On the signs of Fourier coefficients of cusp forms.Ramanujan J. 7 (2003), 269-277. Zbl 1045.11027, MR 2035806, 10.1023/A:1026207515396 |
| Reference:
|
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| Reference:
|
[6] Kohnen, W., Martin, Y.: Sign changes of Fourier coefficients of cusp forms supported on prime power indices.Int. J. Number Theory 10 (2014), 1921-1927. Zbl 1304.11022, MR 3273469, 10.1142/S1793042114500626 |
| Reference:
|
[7] Meher, J., Murty, M. R.: Sign changes of Fourier coefficients of half-integral weight cusp forms.Int. J. Number Theory 10 (2014), 905-914. Zbl 1304.11029, MR 3208866, 10.1142/S1793042114500067 |
| Reference:
|
[8] Meher, J., Shankhadhar, K. D., Viswanadham, G. K.: A short note on sign changes.Proc. Indian Acad. Sci., Math. Sci. 123 (2013), 315-320. Zbl 1281.11043, MR 3102375, 10.1007/s12044-013-0139-2 |
| Reference:
|
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| . |
