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An improvement for the large sieve for square moduli
We establish a result on the large sieve with square moduli. These bounds improve recent results by S. Baier [S. Baier, On the large sieve with sparse sets of moduli, J. Ramanujan Math. Soc. 21 (2006) 279–295] and L. Zhao ...
On primes in quadratic progressions
We verify the Hardy-Littlewood conjecture on primes in quadratic progressions on average. The results in the present paper significantly improve those of a previous paper of the authors.
On the low-lying zeros of Hasse–Weil L-functions for elliptic curves
In this paper, we obtain an unconditional density theorem concerning the low-lying zeros of Hasse-Weil L-functions for a family of elliptic curves. From this together with the Riemann hypothesis for these L-functions, we ...