دانلود کتاب Various Aspects of Multiple Zeta Functions ― in honor of Professor Kohji Matsumoto's 60th birthday

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Preface Program List of Participants Group photo in front of the Graduate School of Mathematics Building -- August 22, 2017 Contents Gautami Bhowmik and Karin Halupczok, Asymptotics of Goldbach representations. -- Dedicated to Kohji Matsumoto -- §1. Introduction §2. Goldbach Conjecture is often true 2.1. Hardy-Littlewood conjecture 2.2. Exceptional Sets 2.3. Average Orders 2.4. Equivalence with RH 2.5. Omega-results §3. Goldbach representations in arithmetic progressions 3.1. Exceptional Sets 3.2. Mean Value 3.3. Equivalence with GRH-DZC §4. Proof of equivalence of RH and Goldbach average §5. Proof of Lemma on the number of exceptions in progressions References [12] [29] Driss Essouabri, On mean values of multivariable complex valued multiplicative functions and applications. -- Dedicated to Professor Kohji Matsumoto on the occasion of his 60th birthday -- §1. Introduction §2. Preliminaries 2.1. Notations 2.2. Preliminaries from convex analysis 2.3. Construction of the mixed volume constant A₀(T;P) §3. Statements of Main Results 3.1. Preliminary constructions 3.2. Main results 3.3. Two simple arithmetical applications of Theorem 4 3.4. An application to the distribution of multivariable additive functions (mod 1) 3.5. Application to multiple global lgusa zeta functions 3.6. Examples with Σ_f not a quadrant §4. Proofs of Lemma 1 and Theorem 3, 4 4.1. Proof of Lemma 1 4.2. Proof of Theorem 3 4.3. Proof of Theorem 4 §5. Proofs of Corollaries 1, 2 and 3 §6. Proof of Theorem 5 and Corollary 4 §7. Proof of Corollary 5 §8. Appendix on Landau's tauberian theorem §9. Appendix on Natural boundary References [18] Katusi Fukuyama, A metric discrepancy result for geometric progression with ratio 3/2. -- Dedicated to Professor Kohji Matsumoto on his 60th birthday -- §1. Introduction §2. Preliminary §3. [0, 1/3) part §4. [1/3, 3/2³) part §5. [4/3², 1/2) part §6. [3/2³, 11/3³) part §7. [11/3³, 87/211), [28/65, 4/3²) part §8. [34/3⁴, 28/65) part §9. [87/211, 101/3⁵) part §10. [278/665, 34/3⁴) part §11. [858/2059, 278/665) part §12 [911/3⁷, 858/2059) part §13. [101/3⁵, 857/2059) part §14. [857/2059, 202/485) part §15. [202/485, 7985/19171) part §16. [7985/19171, 24169/58025) part §17. [24169/58025, 24596/3¹⁰) part §18. [24596/3¹⁰, 72935/175099) part §19. [72935/175099, 73789/3¹¹) part §20. [73789/3¹¹, c), [c, 911/3⁷) part References Ramūnas Garunkštis, Raivydas Šimėnas and Rokas Tamošiūnas, Zeros of derivative of Lerch's zeta-function §1. Introduction §2. Results §3. Zero-free regions and trivial zeros References [5] Yasuaki Hiraoka, Hiroyuki Ochiai and Tomoyuki Shirai, Zeta functions of periodic cubical lattices and cyclotomic-like polynomials §1. Introduction §2. Eigenvalues for periodic cubical complexes 2.1. Eigenvalues of adjacency matrices 2.2. Eigenvalues of Laplacians §3. Zeta functions of periodic cubical complexes §4. Cyclotomic-like polynomials References Roma Kačinskaitė, On the investigation of the Matsumoto zeta-function §1. The Matsumoto zeta-function §2. The Riemann zeta-function 2.1. Bohr-Jessen type results 2.2. Universality §3. First results for the function φ(s) §4. Continuous weighted limit theorems for the function φ(s) §5. Estimates for the number of zeros for linear combinations §6. Two types of discrete limit theorems for the function φ(s) 6.1. Discrete limit theorems of first type 6.2. Discrete limit theorems of second type §7. Joint - continuous and discrete - limit theorems §8. Universality of the function φ(s) §9. Mixed joint universality for a class of zeta-functions: continuous and discrete cases, consequences 9.1. Mixed joint universality: continuous case 9.2. Mixed joint universality: discrete case §10. The biography and scientific activity of Professor Kohji Matsumoto 10.1. Brief biography and first steps in mathematics 10.2. Scientific work § Acknowledgement References [12] [29] [45] [61] Yuichi Kamiya, On hybrid fractal curves of the Heighway and Lévy dragon curves. -- Dedicated to Professor Kohji Matsumoto on the occasion of his 60th birthday -- §1. Introduction and statement of results §2. Proof of Theorem 1.1 §3. Proof of Theorem 1.2 §4. Appendix References [9] Masanobu Kaneko and Hirofumi Tsumura, Zeta functions connecting multiple zeta values and poly-Bernoulli numbers. Dedicated to Professor Kohji Matsumoto, with admiration §1. Introduction §2. Multi-poly-Bernoulli numbers and related zeta functions §3. Relations among ξ, η and multiple zeta functions §4. The function η(k₁, ... ,k_r; s) for nonpositive indices and related topics §5. Zeta functions interpolating multiple zeta values of level 2 References [4] [24] Masanori Katsurada, Complete asymptotic expansions associated with various zeta-functions. -- Dedicated to Professor Kohji Matsumoto on the occasion of his 60th birthday -- §1. Introduction §2. The mean squares of Dirichlet L-functions 2.1. Atkinson's dissection method 2.2. Mellin-Barnes type integrals §3. The mean squares of Hurwitz and Lerch zeta-functions 3.1. The mean square of Hurwitz zeta-functions 3.2. The mean square of Lerch zeta-functions 3.3. Multiple mean square §4. Epstein zeta-functions and Eisenstein series 4.1. Asymptotics for Epstein zeta-functions 4.2. Double holomorphic Eisenstein series and related aspects 4.3. Relevant double series §5. Integral transforms of Lerch zeta-functions 5.1. Laplace-Mellin transforms 5.2. Riemann-Liouville transforms §6. Asymptotic aspects of the Lerch zeta-function in the associated (second) parameter 6.1. Statement of results; asymptotic expansions 6.2. Applications §7. Proofs of our results presented in Section 6 7.1. Preliminary lemmas 7.2. Proofs Theorems 15, 16 and Corollary 15.1 7.3. Proofs of Corollaries 16.2-16.4 7.4. Proofs of Corollaries 15.3, 16.7 and 16.10 References [13] [33] [51] Yasushi Komori, Kohji Matsumoto and Hirofumi Tsumura, An overview and supplements to the theory of functional relations for zeta-functions of root systems §1. Introduction §2. A survey on previous methods §3. Generating Functions (B_{r-1} ⊂ B_r and D_{r-1} ⊂ D_r Cases) 3.1. B_r Case 3.2. D_r Case §4. Generating Functions (A₁² ⊂ A₃ Case) §5. Several examples of functional relations 5.1. B₃ Case 5.2. A₃ Case and D₃ Case §6. Another type of functional relation for ζ₂(s; C₂) References [6] [20] [35] Antanas Laurinčikas, Joint approximation by zeta-functions of cusp forms. -- In honour of Professor Kohji Matsumoto on the occasion of his 60th birthday -- §1. Introduction §2. Probabilistic results §3. Proofs of universality References [14] Junghun Lee, Athanasios Sourmelidis, Jörn Steuding and Ade Irma Suriajaya, The values of the Riemann zeta-function on discrete sets. -- Dedicated to Professor Kohji Matsumoto at the occasion of his 60th Birthday -- §1. Introduction and Statement of the Main Results §2. The Half-Plane of Absolute Convergence §3. The Right Half of the Critical Strip §4. Once More the Right Half of the Critical Strip and Beyond the Critical Line §5. Concluding Remarks References [4] [23] Yasuko Morita, Atsuki Umegaki and Yumiko Umegaki, Bicubic number fields with large class numbers §1. Introduction and main result §2. Bicubic case §3. Generalization References [9] Yasuo Ohno and Yoshitaka Sasaki, Recurrence formulas for poly-Bernoulli polynomials. -- Dedicated to Professor Kohji Matsumoto on the occasion of his 60th birthday -- §1. Introduction §2. Annihilation formulas 2.1. Annihilation formulas and dualities 2.2. Examples §3. Poly-Bernoulli polynomials References Yasuo Ohno and Hirotsugu Wayama, Interpolated multiple zeta functions of Arakawa-Kaneko type. -- Dedicate to Professor Kohji Matsumoto on the occasion of his 60th birthday -- §1. Introduction §2. t-Arakawa-Kaneko multiple zeta function §3. Interpolated Kaneko-Tsumura multiple zeta function References Biswajyoti Saha, Ayyadurai Sankaranarayanan and Yuta Suzuki, An asymptotic formula and some explicit estimates of the counting function of y-friable numbers. -- In honour of Professor Kohji Matsumoto on his sixtieth birthday -- §1. Introduction §2. Notations and Preliminaries §3. Intermediate lemmas and proof of Theorem 1 3.1. Proof of Theorem 1 §4. Proof of the main theorem 4.1. Intermediate lemmas in the small u case 4.2. Completion of the proof of the main theorem §5. Proofs of the intermediate lemmas 5.1. Proof of Lemma 9 5.2. Proof of Lemma 8 5.3. Proof of Lemma 7 5.4. Proof of Lemma 6 5.5. Additional lemmas to prove Lemma 10 5.6. Proof of Lemma 16 5.7. Proof of Lemma 15 5.8. Proof of Lemma 13 5.9. Proof of Lemma 14 5.10. Proof of Lemma 10 5.11. Proof of Lemma 11 §6. Some explicit bounds 6.1. The case 1400 ≤ y ≤ log x 6.2. The case y=log^A x for 1 < A < 2 6.3. The case y=log² x 6.4. The case y=log^A x for A > 2 References [7] Masatoshi Suzuki, Integral operators arising from the Riemann zeta function. -- Dedicated to Professor Kohji Matsumoto at the occasion of his 60th Birthday -- §1. Introduction §2. Proof of Theorem 1 §3. Proof of Theorem 2 §4. Approximate formulas References