Random ordering in modulus of consecutive Hecke eigenvalues of primitive forms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F18%3AA1901XZH" target="_blank" >RIV/61988987:17310/18:A1901XZH - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1112/S0010437X18007455" target="_blank" >http://dx.doi.org/10.1112/S0010437X18007455</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/S0010437X18007455" target="_blank" >10.1112/S0010437X18007455</a>

Result language
angličtina
Original language name
Random ordering in modulus of consecutive Hecke eigenvalues of primitive forms
Original language description
Let tau(.) be the classical Ramanujan tau-function and let k be a positive integer such that T (n) = 0 for 1 <= n <= k/2. (This is known to be true for k < 10(23), and, conjecturally, for all k.) Further, let sigma be a permutation of the set {1,, k}. We show that there exist infinitely many positive integers m such that vertical bar tau(m + sigma(1))vertical bar < vertical bar tau(m)) + sigma(2))vertical bar < ... < vertical bar tau(m + sigma(k))vertical bar. We also obtain a similar result for Hecke eigenvalues of primitive forms of square-free level.
Czech name
—
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
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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