S. Dimitrov

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math.NT2026

Lower bounds on expressions depending on the functions {\boldmath $I ¨ (n)$ }, {\boldmath $I ¨ (n)$ } and {\boldmath $I ¨ (n)$ }, III

S. I. Dimitrov

This work is concerned with the study of lower bounds for various expressions related to the arithmetic functions $I ¨ (n)$ , $I ¨ (n)$ and $I ¨ (n)$ . Several explicit estimates are estab…

math.NT2024

The Bombieri-Vinogradov theorem for primes of the form $p = x^{2} + y^{2} + 1$

S. I. Dimitrov

In this paper, we establish a Bombieri-Vinogradov type result for prime numbers of the form $p = x^{2} + y^{2} + 1$ . The proof is based on the enveloping sieve.

math.NT2024

Barban-Davenport-Halberstam type theorems for exponential sums and Piatetski-Shapiro primes

S. I. Dimitrov

In this paper we establish three Barban-Davenport-Halberstam type theorems. Namely for exponential sums over primes, for Piatetski-Shapiro primes and for exponential sums over Piat…

math.NT2024

Inequalities involving arithmetic functions

S. I. Dimitrov

This paper presents a brief survey of the most important and the most remarkable inequalities involving the basic arithmetic functions.

Lower bounds on expressions depending on the functions {\boldmathI¨(n)}, {\boldmathI¨(n)} and {\boldmathI¨(n)}, III

The Bombieri-Vinogradov theorem for primes of the form p=x2+y2+1

Barban-Davenport-Halberstam type theorems for exponential sums and Piatetski-Shapiro primes

Inequalities involving arithmetic functions

Lower bounds on expressions depending on the functions {\boldmath $I ¨ (n)$ }, {\boldmath $I ¨ (n)$ } and {\boldmath $I ¨ (n)$ }, III

The Bombieri-Vinogradov theorem for primes of the form $p = x^{2} + y^{2} + 1$