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Survey on special values of Artin L-function.January 1991 (has links)
by Ka-hon Yeung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1991. / Bibliography: leaves 155-158. / Chapter 1) --- INTRODUCTION --- p.1 / Chapter 2) --- BACKGROUND MATERIALS AND DEFINITIONS --- p.3 / Chapter §1. --- THE RIEMANN ZETA FUNCTION --- p.3 / Chapter §2. --- THE DEDEKIND ZETA FUNCTION --- p.9 / Chapter §3. --- THE DIRICHLET L-FUNCTION --- p.11 / Chapter §4. --- PLACES AND ABSOLUTE VALUES --- p.13 / Chapter §5. --- THE HECKE L-FUNCTION --- p.14 / Chapter §6. --- CLASS FIELD THEORY --- p.17 / Chapter §7. --- LINEAR REPRESENTATIONS OF FINITE GROUPS --- p.19 / Chapter §8. --- THE ARTIN L-FUNCTION --- p.22 / Chapter 3) --- WORKS OF VARIOUS PEOPLE IN THE EVALUATION OF L-FUNCTIONS --- p.28 / Chapter §1. --- CLASS NUMBER FORMULA --- p.28 / Chapter §2. --- WORKS OF SHINTANI --- p.35 / Chapter §3. --- WORKS OF STARK --- p.65 / Chapter 4) --- STARK'S CONJECTURE --- p.90 / Chapter § 1. --- WORKS OF STARK --- p.90 / Chapter §2. --- WORKS OF TATE --- p.102 / Chapter §3. --- WORKS OF SANDS --- p.132 / NOTE --- p.146 / APPENDIX --- p.153 / BIBLIOGRAPHY --- p.155
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Integral Moments of Quadratic Dirichlet L-functions: A Computational PerspectiveAlderson, Matthew 27 April 2010 (has links)
In recent years, the moments of L-functions has been a topic of growing interest in the field of analytic number theory. New techniques, including applications of Random Matrix Theory and multiple Dirichlet series, have lead
to many well-posed theorems and conjectures for the moments of various L-functions. In this thesis, we theoretically and numerically examine the integral moments of quadratic Dirichlet $L$-functions. In particular, we
exhibit and discuss the conjectures for the moments which result from the applications of Random Matrix Theory, number theoretic heuristics, and the theory of multiple Dirichlet series. In the case of the cubic moment, we further numerically investigate the possible existence of additional lower order main terms.
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Integral Moments of Quadratic Dirichlet L-functions: A Computational PerspectiveAlderson, Matthew 27 April 2010 (has links)
In recent years, the moments of L-functions has been a topic of growing interest in the field of analytic number theory. New techniques, including applications of Random Matrix Theory and multiple Dirichlet series, have lead
to many well-posed theorems and conjectures for the moments of various L-functions. In this thesis, we theoretically and numerically examine the integral moments of quadratic Dirichlet $L$-functions. In particular, we
exhibit and discuss the conjectures for the moments which result from the applications of Random Matrix Theory, number theoretic heuristics, and the theory of multiple Dirichlet series. In the case of the cubic moment, we further numerically investigate the possible existence of additional lower order main terms.
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Elipsinių kreivių L funkcijų išvestinės universalumas / The universality of the derivatives of L-functions of elliptic curvesGasiūnaitė, Vaida 29 January 2013 (has links)
Elipsinių kreivių L funkcijų išvestinės universalumo teoremos įrodymas remiasi ribinėmis teoremomis analizinių funkcijų erdvėje, tikimybinio mato silpno konvergavimo prasme. / The proof of the universality of the derivatives of L-functions of elliptic curves is based on a limit theorem in the sense of weak convergence of probability measures in the space of analytic functions.
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Jungtine universalumo teorema Dirichle L funkcijoms / Joint universality theorem for Dirichlet L-functionsDaukšaitė, Renata 02 July 2012 (has links)
Tegul X dirichlė charakteris moduliu q, s=o+it kompleksinis skaičius. Dirichlė L funkcija L(s, X) pusplokštumėje o>1 yra apibrėžiama Dirichlė eilute. Gerai žinome, kad funkcija L(s, X) kai X nėra pagrindinis charakteris, yra analiziškai pratęsiama į visą kompleksinę plokštum, tai yra, ji yra sveikoji funkcija. Jei X yra pagrindinis, tai tuomet funkcija turi paparastąjį polių su reziduumu. 1975 m S. M. Voroninas atrado labai įdomią funkcijų L(s, X) universalumo savybę. Grubiai kalbant ši savybė reiškia, kad kiekviena analizinė funkcija tam tikroje srityje gali būti norimu tikslumu aproksimuojama L funkcijų postūmiais L(s+it, X). Pastaruoju metu yra žinomas šiek tiek bendresnis teoremos variantas, kai X_1,...,X_r yra Dirichlė charakteriai,tenkinantyts 1 teoremos sąlygas, tačiau šio variano įrodymas nėra niekur paskeltas. Todėl magistro darbo tikslas yra pateikti tokios jungtinės universalumo teoremos Dirichlė L funkcijoms įrodymą. / Let X be a Dirichlet character modulo q, and s=o+it be a complex variable. A Dirichlet L-function L(s,X) is defined, for o>1, by Dirichlet serie and is analitic continued to the whole comples plane. It is knowen that the function L(s,X) is universal in the sense that the shifts L(s+it, X) approximate any analytic function. Also, Dirichlet L-function are jointly collection of given analytic functions. The master work is devoted to the proof of a modern joint universality theorem for Dirichlet L-function. This theorem is knowen,howerver , its proof is not given in literature.We remove this gap, and prove the following theorem.
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Dirichlė L funkcijų universalumas / Universality of Dirichlet L-functionsJančiauskienė, Dovilija 17 July 2014 (has links)
Rusų matematikas S. M. Voroninas įrodė, kad vienos funkcijos pagalba galima aproksimuoti norimu tikslumu tam tikros srities kompleksinėse aibėse bet kurią analizinę funkciją. Tačiau neįrodė 1 teoremos analogo Dirichlė L funkcijoms. Darbo tikslas pateikti šios teoremos pilną įrodymą. / Russian mathematician S.M. Voronin proved, that any function can be approximated to the desired accuracy by one function in a specific sets in complex plane. But failed to theorem 1 analogue Dirichlet L-functions. The aim of this to provide a complete proof of the theorem.
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Noncommutative Iwasawa Main Conjectures for Varieties over Finite FieldsWitte, Malte 10 June 2009 (has links) (PDF)
We state and prove an analogue for varieties over finite fields of T. Fukaya's and K. Kato's version of the noncommutative Iwasawa main conjecture. Moreover, we explain how this statement can be reinterpreted in terms of Waldhausen K-theory.
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The fourth moment of automorphic L-functions at prime power level / Le quatrième moment de fonctions L automorphes de niveau une grande puissance d'un nombre premierBalkanova, Olga 22 April 2015 (has links)
Le résultat principal de cette thèse est une formule asymptotique pour le quatrième moment des fonctions L automorphes de niveau p', où p est un nombre premier et v-x. Il prolonge le travail de Rouymi, qui a calculé les trois premiers moments de niveau p, et il généralise les résultats obtenus en niveau premier par Duke, Friedlander & Iwaniec et Kowalski, Michel & Vanderkam. / The main result of this dissertation is an asymptotic formula for the fourth moment of automorphic L-functions of prime power level p, v-x. This is a continuation of the work of Rouymi, who computed the first three moments at prime power level, and a generalisation of results obtained for prime level by Duke, Friedlander & Iwaniec and Kowalski, Michel & Vanderkam.
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On the construction of twisted triple product p-adic L-functions / 捻れ三重積 p 進 L 関数の構成についてIshikawa, Isao 23 March 2017 (has links)
京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20151号 / 理博第4236号 / 新制||理||1609(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 伊藤 哲史, 教授 池田 保, 教授 雪江 明彦 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM
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Noncommutative Iwasawa Main Conjectures for Varieties over Finite FieldsWitte, Malte 17 November 2008 (has links)
We state and prove an analogue for varieties over finite fields of T. Fukaya''s and K. Kato''s version of the noncommutative Iwasawa main conjecture. Moreover, we explain how this statement can be reinterpreted in terms of Waldhausen K-theory.
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