A common combinatorial principle underlies Riemann's formula, the Chebyshev phenomenon, and other subtle effects in comparative prime number theory. I.
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Displaying 1 – 20 of 414
A conjecture of Erdös in number theory
R. Hall (1976)
Acta Arithmetica
A further note on the P.N.T. error term
Andrew Grant (1987)
Časopis pro pěstování matematiky
A generalisation of Artin's conjecture for primitive roots
K. Matthews (1976)
Acta Arithmetica
A higher rank Selberg sieve and applications
Akshaa Vatwani (2018)
Czechoslovak Mathematical Journal
We develop an axiomatic formulation of the higher rank version of the classical Selberg sieve. This allows us to derive a simplified proof of the Zhang and Maynard-Tao result on bounded gaps between primes. We also apply the sieve to other subsequences of the primes and obtain bounded gaps in various settings.
A mean value theorem of Bombieri's type
E. Fogels (1972)
Acta Arithmetica
A new equidistribution property of norms of ideals in given classes
R. Odoni (1977)
Acta Arithmetica
A new method in the elementary theory of primes
Mohan NAIR (1980/1981)
Seminaire de Théorie des Nombres de Bordeaux
A note on a theorem of Hardy and Littlewood
Stanisław Knapowski, W Staś (1962)
Acta Arithmetica
A note on large gaps between consecutive prime numbers
Cameron L. Stewart (1984/1985)
Groupe d'étude en théorie analytique des nombres
A note on large gaps between prime numbers
Martin Huxley (1980)
Acta Arithmetica
A note on numbers with good factorization properties
W. Narkiewicz (1973)
Colloquium Mathematicae
A note on primes between consecutive powers
Danilo Bazzanella (2009)
Rendiconti del Seminario Matematico della Università di Padova
A note on Selberg sieve
Saverio Salerno (1986)
Acta Arithmetica
A note on small gaps between primes in arithmetic progressions
Deniz A. Kaptan (2016)
Acta Arithmetica
We implement the Maynard-Tao method of detecting primes in tuples to investigate small gaps between primes in arithmetic progressions, with bounds that are uniform over a range of moduli.
A Note on the Differences Between Consecutive Primes.
D.R. Heath-Brown, D.A. Goldston (1984)
Mathematische Annalen
A prime number theorem in the theory of the Riemann zeta function.
Akio Fujii (1979)
Journal für die reine und angewandte Mathematik
A probabilistic setting for prime number theory
M. Wunderlich (1974)
Acta Arithmetica
A Proof of the Prime Number Summation Formula Without Assuming the Riemann Hypothesis.
I.C. Chakravartty (1970)
Aequationes mathematicae
A Proof of the Prime Number Summation Formula Without Assuming the Riemann Hypothesis. (Short Communication).
I.C. Chakravartty (1970)
Aequationes mathematicae
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