This invaluable volume collects papers written by many of the world's top experts on L-functions. It not only covers a wide range of topics from algebraic and analytic number theories, automorphic forms, to geometry and mathematical physics, but also treats the theory as a whole.

The contributions reflect the latest, most advanced and most important aspects of L-functions. In particular, it contains Hida's lecture notes at the conference and at the Eigenvariety semester in Harvard University and Weng's detailed account of his works on high rank zeta functions and non-abelian L-functions.

Contents:

• Quantum Maass Forms (R Bruggeman)
• {cal L}-invariant of p-Adic L-Functions (H Hida)
• Siegel Modular Forms of Weight Three and Conjectural Correspondence of Shimura Type and Langlands Type (T Ibukiyama)
• Convolutions of Fourier Coefficients of Cusp Forms and the Circle Method (M Jutila)
• On an Extension of the Derivation Relation for Multiple Zeta Values (M Kaneko)
• On Symmetric Powers of Cusp Forms on GL₂ (H H Kim)
• Zeta Functions of Root Systems (Y Komori et al.)
• Sums of Kloosterman Sums Revisted (Y Motohashi)
• The Lindelöf Class of L-Functions (K Murty)
• A Proof of the Riemann Hypothesis for the Weng Zeta Function of Rank 3 for the Rationals (M Suzuki)
• Elliptic Curves Arising from the Spectral Zeta Function for Non-Commutative Harmonic Oscillators and Gamma_0(4)-Modular Forms (K Kimoto & M Wakayama)
• A Geometric Approach to L-Functions (L Weng)