A Proof of the Prime Number Summation Formula Without Assuming the Riemann Hypothesis. (Short Communication).
A property of the and functions
A purely analytical lower bound for
We give a simple proof of when is an odd primitiv quadratic Dirichlet character of conductor . In particular we do not use the Dirichlet class-number formula.
A quadratic divisor problem.
A quadratic form with prime variables associated with Hecke eigenvalues of a cusp form
Let be a normalized primitive holomorphic cusp form of even integral weight for the full modular group , and denote its th Fourier coefficient by . We consider the hybrid problem of quadratic forms with prime variables and Hecke eigenvalues of normalized primitive holomorphic cusp forms, which generalizes the result of D. Y. Zhang, Y. N. Wang (2017).
A quantitative lower bound for the greatest prime factor of (ab+1)(bc+1)(ca+1)
A reduction technique in Waring's problem, I
A Remark on a Certain Class of Arithmetic Functions
A remark on a paper written by J. M. De Koninck and A. Ivić.
A remark on Artin's conjecture.
A remark on Chen's theorem
A remark on number-theoretical functions
A remark on the Piatetski-Shapiro-Vinogradov theorem
A remark on uniform 0-estimate for k-free integers.
A sharper bound for the least pair of consecutive k-th power non-residues of non-principal characters (mod p) of order k > 3
A short note on the difference between inverses of consecutive integers modulo .
A sieve approach to the Waring-Goldbach problem. I. Sums of four cubes
A sieve approach to the Waring-Goldbach problem, II On the seven cubes theorem
A special prime divisor of the sequence: .
A statistical density theorem for L-functions with applications