Non-linear twists of \(L\)-functions: a survey

DOI10.1007/S00032-010-0119-2zbMath1275.11127OpenAlexW1965676168MaRDI QIDQ627055

Alberto Perelli

Publication date: 19 February 2011

Published in: Milan Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00032-010-0119-2

zbMATH Keywords

\(L\)-functionsSelberg classconverse theorems

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41)

Related Items (17)

A note on Linnik's approach to the Dirichlet \(L\)-functions ⋮ Twists and resonance of \(L\)-functions. I. ⋮ General $\Omega $-theorems for coefficients of $L$-functions ⋮ Converse theorems: from the Riemann zeta function to the Selberg class ⋮ Internal twists of \(L\)-functions. II ⋮ Classification of \(L\)-functions of degree 2 and conductor 1 ⋮ Twists by Dirichlet characters and polynomial Euler products of \(L\)-functions ⋮ Resonance and rapid decay of exponential sums of Fourier coefficients of a Maass form for \(\mathrm{GL}_m(\mathbb Z)\) ⋮ Forbidden conductors of $L$-functions and continued fractions of particular form ⋮ ON THE STANDARD TWIST OF THE -FUNCTIONS OF HALF-INTEGRAL WEIGHT CUSP FORMS ⋮ SOLVING LINEAR EQUATIONS IN L-FUNCTIONS ⋮ Some remarks on the convergence of the Dirichlet series of \(L\)-functions and related questions ⋮ On a Hecke-type functional equation with conductor \(q=5\) ⋮ A Note on Bessel Twists of L-Functions ⋮ On the Rankin–Selberg convolution of degree 2 functions from the extended Selberg class ⋮ Resonance of automorphic forms for 𝐺𝐿(3) ⋮ The standard twist of $L$-functions revisited

Cites Work

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• On the structure of the Selberg class. VII: \(1<d<2\)
• Linear twists of \(L\)-functions of degree 2 from the Selberg class
• On Riemann's function equation with multiple gamma factors
• A survey of the Selberg class of \(L\)-functions. I
• Unique factorization results for semigroups of \(L\)-functions
• A note on Hecke's functional equation and the Selberg class
• Lectures on a method in the theory of exponential sums
• On the Selberg class of Dirichlet series: Small degrees
• On the structure of the Selberg class. V: \(1<d<5/3\)
• On the structure of the Selberg class. I: \(0\leq d\leq 1\).
• A remark on solutions of functional equations of Riemann's type
• Axiomatic Theory of L-Functions: the Selberg Class
• On the structure of the Selberg class, VI: non-linear twists

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