Sign changes of certain arithmetical function at prime powers
Rishabh Agnihotri; Kalyan Chakraborty
Czechoslovak Mathematical Journal (2021)
- Volume: 71, Issue: 4, page 1221-1228
- ISSN: 0011-4642
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topAgnihotri, Rishabh, and Chakraborty, Kalyan. "Sign changes of certain arithmetical function at prime powers." Czechoslovak Mathematical Journal 71.4 (2021): 1221-1228. <http://eudml.org/doc/298197>.
@article{Agnihotri2021,
abstract = {We examine an arithmetical function defined by recursion relations on the sequence $ \lbrace f(p^k)\rbrace _\{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.},
author = {Agnihotri, Rishabh, Chakraborty, Kalyan},
journal = {Czechoslovak Mathematical Journal},
keywords = {arithmetic function; Dirichlet series; Chebyschev polynomial; modular form},
language = {eng},
number = {4},
pages = {1221-1228},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Sign changes of certain arithmetical function at prime powers},
url = {http://eudml.org/doc/298197},
volume = {71},
year = {2021},
}
TY - JOUR
AU - Agnihotri, Rishabh
AU - Chakraborty, Kalyan
TI - Sign changes of certain arithmetical function at prime powers
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 4
SP - 1221
EP - 1228
AB - We examine an arithmetical function defined by recursion relations on the sequence $ \lbrace f(p^k)\rbrace _{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.
LA - eng
KW - arithmetic function; Dirichlet series; Chebyschev polynomial; modular form
UR - http://eudml.org/doc/298197
ER -
References
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