Journal
LITHUANIAN MATHEMATICAL JOURNAL
Volume 61, Issue 3, Pages 345-372Publisher
SPRINGER
DOI: 10.1007/s10986-021-09530-z
Keywords
zeta functions; distributions; moment generating function
Categories
Funding
- NSERC (Canada)
- European Research Council [670239]
- European Research Council (ERC) [670239] Funding Source: European Research Council (ERC)
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This paper investigates the large deviations of sums of weighted random variables that are approximately independent, with examples from number theory.
In this paper, we investigate the large deviations of sums of weighted random variables that are approximately independent, generalizing and improving some results of Montgomery and Odlyzko. We are motivated by examples arising from number theory, including the sequences p(it), chi(p), chi(d)(p), lambda(f) (p), and Kl(q)(a - n, b), where p ranges over the primes, t varies in a large interval, chi varies among all characters modulo q, chi(d) varies over quadratic characters attached to fundamental discriminants |d| <= x, lambda(f) (n) are the Fourier coefficients of holomorphic cusp forms f of (a large) weight k for the full modular group, and Kl(q)(a, b) are the normalized Kloosterman sums modulo a large prime q, where a, b vary in (Fxdd3d;(q))(x).
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