On polynomials in primes, ergodic averages and monothetic groups

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F24%3AA2503819" target="_blank" >RIV/61988987:17310/24:A2503819 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s00605-024-01948-0" target="_blank" >https://link.springer.com/article/10.1007/s00605-024-01948-0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00605-024-01948-0" target="_blank" >10.1007/s00605-024-01948-0</a>

Result language
angličtina
Original language name
On polynomials in primes, ergodic averages and monothetic groups
Original language description
Let G denote a compact monothetic group, and let rho(x)=alpha kx(k)+...+alpha 1 x+alpha 0, where alpha(0),...,alpha(k) are elements of Gone of which is a generator of G. Let(p(n)) n >= 1denote the sequence of rational prime numbers. Suppose f is an element of L (p) (G)for p >1. It is known that if A (N) f(x):=1 /N (N) & sum; (n=1)f(x+rho(p(n))) (N=1,2,...), then the limit lim(n ->infinity)A(N) f(x)exists for almost all x with respect Haar measure. We show that if G is connected then the limit is integral(G)f d lambda. In the case where G is the a-adic integers, which is a totally disconnected group, the limit is described in terms of Fourier multipliers which are generalizations of Gauss sums.
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
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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