In this paper, we establish large sieve inequalities for power moduli in imaginary quadratic numb... more In this paper, we establish large sieve inequalities for power moduli in imaginary quadratic number fields, extending earlier work of Baier and Bansal [S. Baier and A. Bansal, The large sieve with power moduli for [Formula: see text], Int. J. Number Theory 14 (10) (2018) 2737–2756; Large sieve with sparse sets of moduli for [Formula: see text], Acta Arith. 196 (1) (2020) 17–34] for the Gaussian field.
In this paper we aim to generalize the results in [1, 2, 19] and develop a general formula for la... more In this paper we aim to generalize the results in [1, 2, 19] and develop a general formula for large sieve with characters to powerful moduli that will be an improvement to the result in [19].
We verify the Hardy–Littlewood conjecture on primes in quadratic progressions on average. The res... more 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 by the authors [3].
Abstract. In this paper, we are interested in exploring the cancellation of Hecke eigenvalues twi... more Abstract. In this paper, we are interested in exploring the cancellation of Hecke eigenvalues twisted with an exponential sums whose amplitude is √n at prime arguments. ... In this paper, we are interested in estimating an exponential sum over primes with square root amplitude ...
Neither (5) nor (6) exploits the fact that squares are so sparsely distributed among the integers... more Neither (5) nor (6) exploits the fact that squares are so sparsely distributed among the integers. One deduces that there are about Q 3 rational numbers between 0 and 1 with square denominators and height at most Q 2. Hence, these rational numbers are “on average” Q− 3-spaced. So we should be able to do better.
Abstract. In this paper, we develop a large sieve type inequality with characters to square modul... more Abstract. In this paper, we develop a large sieve type inequality with characters to square moduli. One expects that the result should be weaker than the classical inequality, but, conjecturally at least, not by much. The method is generalizable to higher power moduli. ... It was in 1941 that Ju. V. Linnik [8] originated the idea of large sieve, and he also made application to the distribution of quadratic non-residues. A. Rényi studied the large sieve extensively and made important applications to the Goldbach problem. Refinements in that direction have later been made by many.
In this paper, we establish large sieve inequalities for power moduli in imaginary quadratic numb... more In this paper, we establish large sieve inequalities for power moduli in imaginary quadratic number fields, extending earlier work of Baier and Bansal [S. Baier and A. Bansal, The large sieve with power moduli for [Formula: see text], Int. J. Number Theory 14 (10) (2018) 2737–2756; Large sieve with sparse sets of moduli for [Formula: see text], Acta Arith. 196 (1) (2020) 17–34] for the Gaussian field.
In this paper we aim to generalize the results in [1, 2, 19] and develop a general formula for la... more In this paper we aim to generalize the results in [1, 2, 19] and develop a general formula for large sieve with characters to powerful moduli that will be an improvement to the result in [19].
We verify the Hardy–Littlewood conjecture on primes in quadratic progressions on average. The res... more 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 by the authors [3].
Abstract. In this paper, we are interested in exploring the cancellation of Hecke eigenvalues twi... more Abstract. In this paper, we are interested in exploring the cancellation of Hecke eigenvalues twisted with an exponential sums whose amplitude is √n at prime arguments. ... In this paper, we are interested in estimating an exponential sum over primes with square root amplitude ...
Neither (5) nor (6) exploits the fact that squares are so sparsely distributed among the integers... more Neither (5) nor (6) exploits the fact that squares are so sparsely distributed among the integers. One deduces that there are about Q 3 rational numbers between 0 and 1 with square denominators and height at most Q 2. Hence, these rational numbers are “on average” Q− 3-spaced. So we should be able to do better.
Abstract. In this paper, we develop a large sieve type inequality with characters to square modul... more Abstract. In this paper, we develop a large sieve type inequality with characters to square moduli. One expects that the result should be weaker than the classical inequality, but, conjecturally at least, not by much. The method is generalizable to higher power moduli. ... It was in 1941 that Ju. V. Linnik [8] originated the idea of large sieve, and he also made application to the distribution of quadratic non-residues. A. Rényi studied the large sieve extensively and made important applications to the Goldbach problem. Refinements in that direction have later been made by many.
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