Prime geodesic theorem
Let denote the modular group . In this paper it is proved that . The exponent improves the exponent obtained by W. Z. Luo and P. Sarnak.
A remark on the Piatetski-Shapiro-Vinogradov theorem
A remark on Chen's theorem
Additive problems involving primes of special type
On the upper bound for π₂(x)
On the least almost-prime in arithmetic progression
Let denote an almost-prime with at most prime factors, counted according to multiplicity. Suppose that and are positive integers satisfying . Denote by the least almost-prime which satisfies . It is proved that for sufficiently large , there holds This result constitutes an improvement upon that of Iwaniec (1982), who obtained the same conclusion, but for the range in place of .
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