Titlebook: Irregularities in the Distribution of Prime Numbers; From the Era of Helm János Pintz,Michael Th. Rassias Book 2018 Springer International

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https://doi.org/10.1007/978-3-319-92777-0analytic number theory; approximation theory; probabilistic theory; additive number theory; computationa

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Chains of Large Gaps Between Primes,arge gaps of primes. Recently, with Green and Konyagin, the authors showed that . for sufficiently large .. In this note, we combine the arguments in that paper with the Maier matrix method to show that . for any fixed . and sufficiently large .. The implied constant is effective and independent of ..

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Distribution of Large Gaps Between Primes,We survey some past conditional results on the distribution of large gaps between consecutive primes and examine how the Hardy–Littlewood prime .-tuples conjecture can be applied to this question.

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On the Difference in Values of the Euler Totient Function Near Prime Arguments,We prove unconditionally that for each ., the difference .(.???.)???.(.?+?.) is positive for 50. of odd primes . and negative for 50..

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Sums of Values of Nonprincipal Characters over Shifted Primes,For a nonprincipal character . modulo ., when ., (., .)?=?1, we prove a nontrivial estimate of the form . for the sum of values of . over a sequence of shifted primes.

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