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.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Weights of Partitions and Character Zeros

We classify partitions which are of maximal p-weight for all odd primes p. As a consequence, we show that any non-linear irreducible character of the symmetric and alternating groups vanishes on some element of prime order.

متن کامل

Correlations between Zeros and Supersymmetry

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...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: International Journal of Number Theory

سال: 2022

ISSN: ['1793-7310', '1793-0421']

DOI: https://doi.org/10.1142/s1793042123500069