The fourth moment of quadratic Dirichlet L-functions
نویسندگان
چکیده
منابع مشابه
The Fourth Moment of Dirichlet L-functions
for certain explicitly computable constants ai. The difficult part of extending Ingham’s result to include the lower-order terms is asymptotically evaluating the off-diagonal terms. The family of all primitive Dirichlet L-functions of modulus q is similar in some ways to the Riemann zeta function in t-aspect, but is more difficult to analyze. In 1981, Heath-Brown obtained an asymptotic formula ...
متن کاملThe Fourth Moment of Dirichlet L-functions
Here ∑∗ denotes summation over primitive characters χ (mod q), φ(q) denotes the number of primitive characters (mod q), and ω(q) denotes the number of distinct prime factors of q. Note that φ(q) is a multiplicative function given by φ(p) = p − 2 for primes p, and φ(p) = p(1 − 1/p) for k ≥ 2 (see Lemma 1 below). Also note that when q ≡ 2 (mod 4) there are no primitive characters (mod q), and so ...
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For χ a Dirichlet character (mod q), the moments of L(s, χ) have many applications, for example to the distribution of primes in the arithmetic progressions to modulus q. The asymptotic formula of the fourth power moment in the q-aspect has been obtained by Heath-Brown [1], for q prime, and more recently by Soundararajan [5] for general q. Following Soundararajan’s work, Young [7] pushed the re...
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متن کاملReal zeros of quadratic Dirichlet L - functions
A small part of the Generalized Riemann Hypothesis asserts that L-functions do not have zeros on the line segment ( 2 , 1]. The question of vanishing at s = 2 often has deep arithmetical significance, and has been investigated extensively. A persuasive view is that L-functions vanish at 2 either for trivial reasons (the sign of the functional equation being negative), or for deep arithmetical r...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2020
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-020-02609-2