A weaker but simpler sieve inequality
We discuss a cancellation property of sieve weights, one that is applicable to the distribution of primes and almost-primes in very short intervals.
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arXiv subjects
John B. Friedlander
Publications and source records attributed to John B. Friedlander.
Twin Primes Via Exceptional Characters
We give an account of the arguments that lead from the assumption of the existence of exceptional characters to the asymptotics in related ranges for the counting function of twin primes.
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On Waring's problem: two squares and three biquadrates
We investigate sums of mixed powers involving two squares and three biquadrates. In particular, subject to the truth of the Generalised Riemann Hypothesis and the Elliott-Halberstam Conjecture, we show that all large natural numbers n with 8 not dividing n, n not congruent to 2 modulo 3, and n not congruent to 14 modulo 16, are the sum of 2 squares and 3 biquadrates.
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Products in Residue Classes
We consider a problem of P. Erdos, A. M. Odlyzko and A. Sarkozy about the representation of residue classes modulo m by products of two not too large primes. While it seems that even the Extended Riemann Hypothesis is not powerful enough to achieve the expected results, here we obtain some unconditional results ``on average'' over moduli m and residue classes modulo m and somewhat stronger results when the average is restricted to prime moduli m = p. We also consider the analogous question wherein the primes are replaced by easier sequences so, quite naturally, we obtain much stronger results.
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Integers without divisors from a fixed arithmetic progression
Let a be an integer and q a prime number. In this paper, we find an asymptotic formula for the number of positive integers n < x with the property that no divisor d > 1 of n lies in the arithmetic progression a modulo q.
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