On cyclotomic factors of polynomials related to modular forms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F19%3AA20023MW" target="_blank" >RIV/61988987:17310/19:A20023MW - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007%2Fs11139-017-9980-8" target="_blank" >https://link.springer.com/article/10.1007%2Fs11139-017-9980-8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11139-017-9980-8" target="_blank" >10.1007/s11139-017-9980-8</a>

Result language
angličtina
Original language name
On cyclotomic factors of polynomials related to modular forms
Original language description
The Fourier coefficients of powers of the Dedekind eta function can be studied simultaneously. The vanishing of the coefficients varies from super lacunary (Euler, Jacobi identities) and lacunary (CM forms) to non-vanishing (Lehmer conjecture for the Ramanujan numbers). We study polynomials of degreen, whose roots control the vanishing of the nth Fourier coefficients of such powers. We prove that every root of unity appearing as any root of these polynomials has to be of order 2.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA17-02804S" target="_blank" >GA17-02804S: Properties of number sequences and their applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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