Axiomatic Theory of L-Functions: the Selberg Class

DOI10.1007/978-3-540-36364-4_4zbMATH Open1147.11050OpenAlexW164505209MaRDI QIDQ3511716

Jerzy Kaczorowski

Publication date: 11 July 2008

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-540-36364-4_4

zbMATH Keywords

\(L\)-functionszeta-functionsSelberg class

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36)

Related Items (61)

Zeros of derivatives of 𝐿-functions in the Selberg class on ℜ(𝑠)<1/2 ⋮ Tong-type identity and the mean square of the error term for an extended Selberg class ⋮ A note on Linnik's approach to the Dirichlet \(L\)-functions ⋮ Zeros of the extended Selberg class zeta-functions and of their derivatives ⋮ Zeros of combinations of Euler products for \(\sigma > 1\) ⋮ Twists and resonance of \(L\)-functions. I. ⋮ Unnamed Item ⋮ General $\Omega $-theorems for coefficients of $L$-functions ⋮ The Li–Sekatskii coefficients for the Selberg class ⋮ On some complex explicit formulæ connected with Dirichlet coefficients of inverses of special type L-functions from the Selberg class ⋮ The Mean Values of the Riemann Zeta-Function on the Critical Line ⋮ Selberg's orthogonality conjecture and symmetric power \(L\)-functions ⋮ Converse theorems: from the Riemann zeta function to the Selberg class ⋮ Classification of \(L\)-functions of degree 2 and conductor 1 ⋮ Zeta functions of finite fields and the Selberg class ⋮ Twists by Dirichlet characters and polynomial Euler products of \(L\)-functions ⋮ On the density of zeros of linear combinations of Euler products for \(\sigma>1\) ⋮ Amplitude-like functions from entire functions ⋮ Forbidden conductors of $L$-functions and continued fractions of particular form ⋮ On Ihara’s conjectures for Euler–Kronecker constants ⋮ Non-linear twists of \(L\)-functions: a survey ⋮ The joint universality for pairs of zeta functions in the Selberg class ⋮ On the oscillatory behavior of certain arithmetic functions associated with automorphic forms ⋮ On the structure of the Selberg class. VII: \(1<d<2\) ⋮ Linear twists of \(L\)-functions of degree 2 from the Selberg class ⋮ ON THE STANDARD TWIST OF THE -FUNCTIONS OF HALF-INTEGRAL WEIGHT CUSP FORMS ⋮ Unique factorization results for semigroups of \(L\)-functions ⋮ Value distribution for the derivatives of the logarithm of \(L\)-functions from the Selberg class in the half-plane of absolute convergence ⋮ ON INTERPOLATION FUNCTIONS FOR GENERALIZED Li COEFFICIENTS IN THE SELBERG CLASS ⋮ On relations equivalent to the generalized Riemann hypothesis for the Selberg class ⋮ SOLVING LINEAR EQUATIONS IN L-FUNCTIONS ⋮ Some remarks on the convergence of the Dirichlet series of \(L\)-functions and related questions ⋮ Some remarks on the unique factorization in certain semigroups of classical \(L\)-functions ⋮ On Li's criterion for the Riemann hypothesis for the Selberg class ⋮ The Li criterion and the Riemann hypothesis for the Selberg class. II ⋮ Some remarks on infinite products of \(L\)-functions ⋮ Algebraic independence of logarithmic singularities of some complex functions ⋮ Omega theorems related to the general Euler totient function ⋮ Ω-estimates related to irreducible algebraic integers ⋮ Voros-Li type criterion for a class of \(L\)-functions ⋮ On properties of certain special zeros of functions in the Selberg class ⋮ Large Values of the Zeta-Function on the Critical Line ⋮ On a generalization of the Euler totient function ⋮ On a generalization of the Euler totient function ⋮ Twists by Dirichlet characters and polynomial Euler products of \(L\)-functions. II ⋮ Variants of the Li-type criteria for the generalized Riemann hypothesis ⋮ \(L\)-functions of degree \(2\) and conductor \(1\): underlying ideas and a generalisation ⋮ Bipartite and directed scale-free complex networks arising from zeta functions ⋮ On the mean square of an arithmetical error term of the Selberg class in short intervals ⋮ On the Rankin–Selberg convolution of degree 2 functions from the extended Selberg class ⋮ Unnormalized differences between zeros ofL-functions ⋮ A note on the degree conjecture for the Selberg class ⋮ A uniqueness property of general Dirichlet series ⋮ A remark on uniqueness of $L$-functions in the extended Selberg class ⋮ On the linear twist of degree \(1\) functions in the extended Selberg class ⋮ Asymptotics for a class of arithmetic functions ⋮ A note on Hecke's functional equation and the Selberg class ⋮ On the Speiser equivalent for the Riemann hypothesis ⋮ On Landau–Siegel zeros and heights of singular moduli ⋮ A proof of Newman’s conjecture for the extended Selberg class ⋮ The standard twist of $L$-functions revisited

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