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Tagged with measure-theory analytic-number-theory
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When does the measure integral of the form $\int_{\log(S)} f \,d \mu$ exist?
When does the measure integral of the form $\int_{\log(S)} f \,d \mu$ exist?
Here $\mu$ can be any measure (Lebesgue, Borel, Haar etc), $f$ is a measurable function, $S$ is any measurable set with ...
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2
votes
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Exchanging the order of integration without Fubini-Tonnelli in an integral related to Waring's problem
My question relates to the evaluation of the singular integral for Waring's problem, following pp. 460 of Iwaniec and Kowalski's "Analytic Number Theory".
Background:
There, we are ...
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Convergence of an integral over the primes
Does the following integral converge? If so, is it nonzero? What can we say about the integral as $x\to \infty?$
$$\int_{I} \frac{u-u\log{p_u}}{(p_u)^2}du$$
where $I= \{p \leq x | p\text{ prime}\}$ ...
