Correlations of sieve weights and distributions of zeros
نویسندگان
چکیده
In this note, we give two small results concerning the correlations of Selberg sieve weights. We then use these estimates to derive a new (conditional) lower bound on variance primes in short intervals, and also so-called “form factor” for pair zeros Riemann zeta function. Our bounds ultimately rely Bettin–Chandee trilinear Kloosterman fractions.
منابع مشابه
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In our previous work [BSZ2], we proved that the correlation functions for simultaneous zeros of random generalized polynomials have universal scaling limits and we gave explicit formulas for pair correlations in codimensions 1 and 2. The purpose of this paper is to compute these universal limits in all dimensions and codimensions. First, we use a supersymmetry method to express the n-point corr...
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2022
ISSN: ['1793-7310', '1793-0421']
DOI: https://doi.org/10.1142/s1793042123500069