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Refinements of Erdős's irrationality criterion for certain sparse infinite series
Hajime Kaneko, Yuta Suzuki, Yohei Tachiya
In this paper, we establish new irrationality criteria for certain sparse power series. As applications of these criteria, we generalize a result of Erdős and obtain several irrati…
The Zsiflaw--Legeis theorem for arbitrary bases
Gautami Bhowmik, Yuta Suzuki
In this paper, we prove analogues of the Dirichlet theorem on arithmetic progressions and the Siegel--Walfisz theorem for the digital reverses of primes for arbitrary bases, which…
On Telhcirid's theorem on arithmetic progressions
Gautami Bhowmik, Yuta Suzuki
In this paper, we study the distribution of the digital reverses of prime numbers, which we call the "reversed primes". We prove the infinitude of reversed primes in any arithmetic…
Asymptotic formula for the sum of a prime and a square-full number in short intervals
Fumi Ogihara, Yuta Suzuki
Let be a representation function for the sum of a prime and a square-full number. In this article, we prove an asymptotic formula for the sum of $R_{m,…
Relatively prime pairs in the Piatetski-Shapiro sequences
Yuta Suzuki
In this paper, we prove an asymptotic formula for the number of relatively prime pairs in the Piatetski-Shapiro sequence of arbitrarily large order. This improves the result of Pim…
Some remarks on the -sequence
Kota Saito, Yuta Suzuki, Wataru Takeda +1
After the work of Bordellès, Dai, Heyman, Pan and Shparlinki (2018) and Heyman (2019), several authors studied the averages of arithmetic functions over the sequence and th…
Counting relatively prime pairs of palindromes
Hirotaka Kobayashi, Yuta Suzuki, Ryota Umezawa
For a given base , a positive integer is called a palindrome if its base expansion reads the same backwards as forwards. In this paper, we give an asymptotic formula for…
Distribution of rational points on random Fano hypersurfaces
Yohsuke Matsuzawa, Yuta Suzuki
We prove an asymptotic formula for the average number of rational points on Fano hypersurfaces that are contained in a small ball centered at a given adelic point. We also prove an…