CONTENTS -- Preface -- Recent progress on the quantitative arithmetic of del Pezzo surfaces Tim D. Browning -- 1. Introduction -- Acknowledgements -- 2. Geometry of V0 -- 3. Overview of the proof -- 3.1. Reduction to conics of low height -- 3.2. Parametrisation of the conics -- 3.3. Lattice point counting in the plane -- 3.4. Divisor problem for binary forms -- 3.5. Comparison with Peyre's constant -- 4. Further exploration -- References -- Additive representation in thin sequences, VIII: Diophantine inequalities in review Jorg Brudern, Koichi Kawada and Trevor D. Wooley -- 1. Theme and results -- 1.1. Diophantine inequalities -- 1.2. Additive cubic forms -- 1.3. Linear forms in primes -- 1.4. Further applications -- 1.5. A related diophantine inequality -- 2. The Fourier transform method -- 2.1. Some classical integrals -- 2.2. Counting solutions of diophantine inequalities -- 2.3. Weighted counting -- 2.4. The central interval -- 2.5. The interference principle -- 3. Classical mean square methods -- 3.1. Plancherel's identity -- 3.2. Some mean values -- 3.3. The amplification technique -- 3.4. Linear forms in primes -- 3.5. Bessel's inequality -- 4. Semi-classical averaging -- 4.1. Another mean square approach -- 4.2. Exponential sums over test sequences -- 4.3. Potential applications -- 5. Fourier analysis of exceptional sets -- 5.1. An illustrative example -- 5.2. A quadratic average -- 5.3. Some brief heckling -- 5.4. An inequality involving quadratic polynomials -- 5.5. An application of Vinogradov's method -- 5.6. Linear forms in primes, yet again -- 6. Outstanding arts -- 6.1. Smooth cubic Weyl sums -- 6.2. Senary cubic forms -- 6.3. Two technical estimates -- 6.4. The lower bound variant -- 6.5. An auxiliary inequality -- 6.6. Additive forms of large degree -- 6.7. Proof of Theorem 1.8 -- 6.8. Proof of Theorem 1.9.

7. An appendix on inhomogenous polynomials -- 7.1. The counting integral -- 7.2. The central interval -- 7.3. The complementary compositum -- Acknowledgements -- References -- Recent progress on dynamics of a special arithmetic function Chaohua Jia -- 1. Introduction -- 2. Dynamics of the w function -- 3. Inverse problem -- 4. The sketch of the proof of Theorem 3.5 -- 5. Acknowledgements -- References -- Some Diophantine problems arising from the isomorphism problem of generic polynomials Akinari Hoshi and Katsuya Miyake -- 1. Introduction -- 2. Some results: the cubic case -- 3. A parametric family of Thue equations -- 4. The case of D4 -- 5. Numerical examples: the case of C4 -- 6. Numerical examples: the case of D5 -- 7. Appendix -- References -- A statistical relation of roots of a polynomial in different local fields II Yoshiyuki Kitaoka -- 1. Introduction and Conjectures -- 1.1. Irreducible case -- 1.2. Reducible case -- 1.3. Generalization -- 2. Numerical data -- 2.1. n = 3 -- 2.3. n = 5 -- 2.4. n = 6 -- 2.5. n = 7 -- 2.6. n = 8 -- 2.7. n = 9 -- 2.8. n = 10 -- 2.9. n = 12 -- 2.10. n = 15 -- 2.11. Other examples -- References -- Generalized modular functions and their Fourier coefficients Winfried Kohnen -- 1. Introduction -- 2. Generalized modular functions, main features of the theory and examples -- 3. Fourier coefficients of GMF's -- References -- Functional relations for zeta-functions of root systems Yasushi Komori, Kohji Matsumoto and Hirofumi Tsumura -- 1. Introduction -- 2. A method to evaluate the Riemann zeta-function -- 3. Functional relations for ζ2(s1, s2, s3 -- A2) -- 4. Another method to construct functional relations for Dirichlet series -- 5. A general form of functional relations -- 6. Some lemmas for explicit construction of functional relations -- 7. Functional relations for ζ3(s -- A3) -- 8. Functional relations for ζ2(s.

C2) -- 9. Functional relations for ζ3(s -- B3) and for ζ3(s -- C3) -- References -- A quick introduction to Maass forms Jianya Liu -- 1. Introduction -- 1.1. The aim of the paper -- 1.2. Notation -- 2. Maass forms for SL2(Z) -- 3. Analytic continuation of Eisenstein series -- 3.1. Fourier expansion of Maass forms -- 3.2. Analytic continuation of Eisenstein series -- 4. Spectral decomposition of non-Euclidean Laplacian -- 5. Hecke's theory for Maass forms -- 6. The Kuznetsov trace formula -- 7. Automorphic L-functions -- 7.1. Automorphic L-functions attached to Maass forms -- 7.2. Rankin-Selberg automorphic L-functions -- 8. Maass forms for Γ0(N) and their L-functions -- 8.1. Maass forms for Γ0(N) -- 8.2. Automorphic L-functions for Maass forms for Γ0(N) -- 9. Linnik-type problems -- 9.1. Linnik's original problem -- 9.2. A Linnik-type problem for Maass forms -- 9.3. A Linnik-type problem for holomorphic forms -- 9.4. Linnik-type problems for higher rank groups -- Acknowledgements. -- References -- The number of non-zero coefficients of a polynomial-solved and unsolved problems Andrzej Schinzel -- References -- Open problems on exponential and character sums Igor E. Shparlinski -- 1. Introduction -- 2. Notation -- 3. Problems -- 3.1. Exponential functions -- 3.2. Short character sums -- 3.3. Smooth numbers, S-units and primes -- 3.4. Combinatorial sequences -- 3.5. Polynomial discriminants -- 3.6. Arithmetic functions -- 3.7. Beatty sequences -- 3.8. Sparse polynomials -- 3.9. Nonlinear recurrence sequences -- 3.10. Evaluation of Kloosterman sums -- Acknowledgements -- References -- Errata to "A general modular relation in analytic number theory" Haruo Tsukada -- Bibliography on determinantal expressions of relative class numbers of imaginary abelian number fields Ken Yamamura -- References -- Author Index.