GOLDBACH REPRESENTATIONS IN ARITHMETIC PROGRESSIONS AND ZEROS OF DIRICHLET L ‐FUNCTIONS

DOI10.1112/S0025579318000323zbMath1432.11136arXiv1704.06103MaRDI QIDQ4683856

Yuta Suzuki, Gautami Bhowmik, Kohji Matsumoto, Karin Halupczok

Publication date: 26 September 2018

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.06103

zbMATH Keywords

arithmetic progressionsum of primesDirichlet \(L\)-functions

Mathematics Subject Classification ID

Goldbach-type theorems; other additive questions involving primes (11P32) Other Dirichlet series and zeta functions (11M41) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (15)

Conditional Bounds on Siegel Zeros ⋮ Refined Goldbach Conjectures with Primes in Progressions ⋮ The Barban–Davenport–Halberstam theorem for a restricted set of arithmetic progressions ⋮ On the conditional bounds for Siegel zeros ⋮ ON AN AVERAGE GOLDBACH REPRESENTATION FORMULA OF FUJII ⋮ Exceptional zeros, sieve parity, Goldbach ⋮ Double Dirichlet series associated with arithmetic functions. II ⋮ A Montgomery-Hooley theorem for the number of Goldbach representations ⋮ An M-function associated with Goldbach's problem ⋮ A survey on the theory of multiple Dirichlet series with arithmetical coefficients as numerators ⋮ Some explicit formulas for partial sums of Möbius functions ⋮ Cesàro averages for Goldbach representations with summands in arithmetic progressions ⋮ Average Goldbach and the quasi-Riemann hypothesis ⋮ Double Dirichlet series associated with arithmetic functions ⋮ Exceptional zeros and the Goldbach problem

Cites Work

• Goldbach's conjecture in arithmetic progressions: number and size of exceptional prime moduli
• Meromorphic continuation of the Goldbach generating function
• On the distribution of imaginary parts of zeros of the Riemann zeta function. II
• Average Goldbach and the quasi-Riemann hypothesis
• Refinements of Goldbach's conjecture, and the generalized Riemann hypothesis
• A large sieve density estimate near \(\sigma = 1\)
• A mean value of the representation function for the sum of two primes in arithmetic progressions
• Mean representation number of integers as the sum of primes
• An additive problem of prime numbers
• CONVOLUTIONS OF THE VON MANGOLDT FUNCTION AND RELATED DIRICHLET SERIES
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