## Zeros of Eisenstein series quadratic class numbers and

Coleman's power series and Wiles' reciprocity for rank 1. Fractional Power Series and Pairings on Drinfeld Modules Created Date: 20160730200410Z, pdf. K1 of products of Drinfeld modular curves and special values of L-functions. Compositio Mathematica, 2010. Ramesh Sreekantan. Download with Google Download with Facebook or download with email. K1 of products of Drinfeld modular curves and special values of L-functions. Download..

### [PDF] Download Number Fields And Function Fields Two

Hypergeometric Functions and Carlitz Differential. These invited articles by leading researchers in the field explore various aspects of the parallel worlds of function fields and number fields. Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives., We construct a pairing for Drinfeld modules which behaves in many ways like the Weil pairing on abelian varieties. In addition, our results let us describe the topological module structure of the kernel of the adjoint exponential function of a Drinfeld module. We conclude with a few unanswered questions. 2. The rings Pand Fof fractional power.

Many of these results extend to non-linear fractional power series. We apply these results to construct a Drinfeld module analogue of the Weil pairing, and to describe the topological module structure of the kernel of the adjoint exponential of a Drinfeld module. Arithmetic over Function Fields (a Cohomological Approach) Gebhard BВЁockle Institute for Experimental Mathematics, EllernstraГџe 29, elliptic curves on the one and Drinfeld modules on the other hand. there is a unique power series e

larity of Drinfeld modules of rank 1 deп¬Ѓned over the п¬Ѓeld of rational functions Key words and phrases. A-expansions, twisting, congruences, Eisenstein series, Drinfeld mod-ular forms, modularity. The author is supported by the Alexander von Humboldt Foundation. 1. will have a power series вЂ¦ numbers (except the nonpositive integers) by knowing only the value of the gamma function between 1 and 2. Table 2 contains the gamma function for arguments between 1 and 1.99. To illustrate, the following three examples show how to evaluate the gamma function for positive integers, fractional positive numbers and a negative noninteger values.

uniformization of Drinfeld modules and the related analytic functions (section 2) and report on the structure of the ring of modular forms in the classical (section 1) and the Drinfeld case (section 3), and on the role played by the respective Eisenstein series, discriminant, and j-invariant functions. In the fourth section, we give a brief ZERO DISTRIBUTION AND DECAY AT INFINITY OF DRINFELD MODULAR COEFFICIENT FORMS ERNST-ULRICH coe cients of the \de ning equations" of Drinfeld modules, Eisenstein series, (coe cients of the exponential functions of rank-2 lattices), coe cients of the division polynomials of Drinfeld modules. As in the case of classical elliptic modular

A survey of Drinfeld modular forms 25.03.97 G. Cornelissen 1 The possibility of a theory of modular forms for function п¬Ѓelds was perhaps implicit in Drin-feldвЂ™s original work, but the notion was only really introduced by Goss and Gekeler in the beginning of the eighties. A lot of it developped along вЂњclassicalвЂќ lines (by the word вЂњclassi- Many of these results extend to non-linear fractional power series. We apply these results to construct a Drinfeld module analogue of the Weil pairing, and to describe the topological module structure of the kernel of the adjoint exponential of a Drinfeld module. 1.

### Coleman's power series and Wiles' reciprocity for rank 1

Fractional Power Series and Pairings on Drinfeld Modules. These invited articles by leading researchers in the field explore various aspects of the parallel worlds of function fields and number fields. Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives., uniformization of Drinfeld modules and the related analytic functions (section 2) and report on the structure of the ring of modular forms in the classical (section 1) and the Drinfeld case (section 3), and on the role played by the respective Eisenstein series, discriminant, and j-invariant functions. In the fourth section, we give a brief.

A Hypothesis Testing Approach for Topology Error Detection. Arithmetic over Function Fields (a Cohomological Approach) Gebhard BВЁockle Institute for Experimental Mathematics, EllernstraГџe 29, elliptic curves on the one and Drinfeld modules on the other hand. there is a unique power series e, For the Carlitz module, this was proven by AnglГЁs: his paper [1] follows the approach of [10, Chapter 9]. In the present paper we introduce the formalism of ColemanвЂ™s power series in the additive setting of (formal) rank 1 Drinfeld modules..

### COLEMANвЂ™S POWER SERIES AND WILESвЂ™ RECIPROCITY FOR

David Goss' Personal Homepage Ohio State University. arXiv:math/0405542v1 [math.NT] 28 May 2004 Strongly Nonlinear Differential Equations with Carlitz Derivatives over a Function Field ANATOLY N. KOCHUBEIв€— Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska 3, Kiev, 01601 Ukraine https://fr.wikipedia.org/wiki/Liste_des_conf%C3%A9rences_pl%C3%A9ni%C3%A8res_des_congr%C3%A8s_internationaux_des_math%C3%A9maticiens Elementary divisors of reductions of generic Drinfeld modules BY ANDREW MICHAEL SHULMAN B.S. (Carroll University) 2004 M.S. (University of Wisconsin - Milwaukee) 2006 THESIS Submitted as partial ful llment of the requirements for the degree of Doctor of Philosophy in Mathematics in the Graduate College of the University of Illinois at Chicago, 2011.

new characterizations involving Moore determinants, and an application to the Weil pairing on Drinfeld modules. We also deп¬Ѓne Drinfeld modular functions of non-zero type and provide a moduli interpretation of these. 1 Drinfeld modular forms We start with a brief introduction to Drinfeld modular forms, see e.g. [7] for more details. Description: The Journal of the American Mathematical Society, begun in 1988, is published quarterly. It contains research articles of the highest quality in all areas of pure and applied mathematics.

Description: The Journal of the American Mathematical Society, begun in 1988, is published quarterly. It contains research articles of the highest quality in all areas of pure and applied mathematics. For the Carlitz module, this was proven by AnglГЁs: his paper [1] follows the approach of [10, Chapter 9]. In the present paper we introduce the formalism of ColemanвЂ™s power series in the additive setting of (formal) rank 1 Drinfeld modules.

GossL-functions Peter Bruin Seminar on Drinfeld modules 14 and 21 October 2015 1. Introduction 1.1. Motivation The purpose of this talk is to introduce Goss L-functions. Many of these results extend to non-linear fractional power series. We apply these results to construct a Drinfeld module analogue of the Weil pairing, and to describe the topological module structure of the kernel of the adjoint exponential of a Drinfeld module.

larity of Drinfeld modules of rank 1 deп¬Ѓned over the п¬Ѓeld of rational functions Key words and phrases. A-expansions, twisting, congruences, Eisenstein series, Drinfeld mod-ular forms, modularity. The author is supported by the Alexander von Humboldt Foundation. 1. will have a power series вЂ¦ A survey of Drinfeld modular forms 25.03.97 G. Cornelissen 1 The possibility of a theory of modular forms for function п¬Ѓelds was perhaps implicit in Drin-feldвЂ™s original work, but the notion was only really introduced by Goss and Gekeler in the beginning of the eighties. A lot of it developped along вЂњclassicalвЂќ lines (by the word вЂњclassi-

## Formal vector spaces over a local eld of positive

FRACTIONAL POWER SERIES AND PAIRINGS ON DRINFELD. Forced Lattice Vibrations -- A Videotext Percy Deift, Thomas Kriecherbauer and Stephanos Venakides MSRI Preprint #1995-003. Note: This is the textbook part of this work., ZERO DISTRIBUTION AND DECAY AT INFINITY OF DRINFELD MODULAR COEFFICIENT FORMS ERNST-ULRICH coe cients of the \de ning equations" of Drinfeld modules, Eisenstein series, (coe cients of the exponential functions of rank-2 lattices), coe cients of the division polynomials of Drinfeld modules. As in the case of classical elliptic modular.

### Properties of the Gamma Function

Hypergeometric Functions and Carlitz Differential. Many of these results extend to non-linear fractional power series. We apply these results to construct a Drinfeld module analogue of the Weil pairing, and to describe the topological module structure of the kernel of the adjoint exponential of a Drinfeld module., GossL-functions Peter Bruin Seminar on Drinfeld modules 14 and 21 October 2015 1. Introduction 1.1. Motivation The purpose of this talk is to introduce Goss L-functions..

a of a \generic" Drinfeld module Лљ, and are thus referred to as coe cient forms. We succeed in determining the absolute values jzjof the zeroes zof aвЂ k in F (Theorem 5.1) as well as of the associated jj(z)j(Theorem 4.11). In contrast with the case of Eisenstein series (but similar to para-Eisenstein series), these 10-6-2014В В· B. Poonen, вЂњFractional power series and pairings on Drinfeld modules,вЂќ Journal of the American Mathematical Society, vol. 9, no. 3, pp. 783вЂ“812, 1996. View at Publisher В· View at Google Scholar В· View at Zentralblatt MATH В· View at MathSciNet В· View at Scopus

Arithmetic over Function Fields (a Cohomological Approach) Gebhard BВЁockle Institute for Experimental Mathematics, EllernstraГџe 29, elliptic curves on the one and Drinfeld modules on the other hand. there is a unique power series e A survey of Drinfeld modular forms 25.03.97 G. Cornelissen 1 The possibility of a theory of modular forms for function п¬Ѓelds was perhaps implicit in Drin-feldвЂ™s original work, but the notion was only really introduced by Goss and Gekeler in the beginning of the eighties. A lot of it developped along вЂњclassicalвЂќ lines (by the word вЂњclassi-

Many of these results extend to non-linear fractional power series. We apply these results to construct a Drinfeld module analogue of the Weil pairing, and to describe the topological module structure of the kernel of the adjoint exponential of a Drinfeld module. AN INTRODUCTION TO INVARIANTS AND MODULI 41 G. Laumon Cohomology of Drinfeld modular varieties I 42 E.B. Davies Spectral theory and differential operators Power series rings 61 (b) Valuation rings 63 2.5 A diversion: rings of invariants which are not п¬Ѓnitely generated 68

larity of Drinfeld modules of rank 1 deп¬Ѓned over the п¬Ѓeld of rational functions Key words and phrases. A-expansions, twisting, congruences, Eisenstein series, Drinfeld mod-ular forms, modularity. The author is supported by the Alexander von Humboldt Foundation. 1. will have a power series вЂ¦ pdf. K1 of products of Drinfeld modular curves and special values of L-functions. Compositio Mathematica, 2010. Ramesh Sreekantan. Download with Google Download with Facebook or download with email. K1 of products of Drinfeld modular curves and special values of L-functions. Download.

associated to the Drinfeld A-module r. We show that this module is п¬Ѓnitely generated and consists of the fractional ideals of A relatively prime to m, such that yj A = c. The Goss L-function for y is deп¬Ѓned to be The power series S(tm;z):=exp Many of these results extend to non-linear fractional power series. We apply these results to construct a Drinfeld module analogue of the Weil pairing, and to describe the topological module structure of the kernel of the adjoint exponential of a Drinfeld module. 1.

COLEMANвЂ™S POWER SERIES AND WILESвЂ™ RECIPROCITY FOR RANK 1 DRINFELD MODULES FRANCESC BARS, IGNAZIO LONGHI Abstract. We introduce the formalism of ColemanвЂ™s power series for rank 1 Drinfeld modules and apply it to formulate and prove the analogue of WilesвЂ™ explicit reciprocity law in this setting. 1. Introduction associated to the Drinfeld A-module r. We show that this module is п¬Ѓnitely generated and consists of the fractional ideals of A relatively prime to m, such that yj A = c. The Goss L-function for y is deп¬Ѓned to be The power series S(tm;z):=exp

larity of Drinfeld modules of rank 1 deп¬Ѓned over the п¬Ѓeld of rational functions Key words and phrases. A-expansions, twisting, congruences, Eisenstein series, Drinfeld mod-ular forms, modularity. The author is supported by the Alexander von Humboldt Foundation. 1. will have a power series вЂ¦ 10-6-2014В В· B. Poonen, вЂњFractional power series and pairings on Drinfeld modules,вЂќ Journal of the American Mathematical Society, vol. 9, no. 3, pp. 783вЂ“812, 1996. View at Publisher В· View at Google Scholar В· View at Zentralblatt MATH В· View at MathSciNet В· View at Scopus

### AMS Journal of the American Mathematical Society

ZERO DISTRIBUTION AND DECAY AT INFINITY OF DRINFELD. Description: The Journal of the American Mathematical Society, begun in 1988, is published quarterly. It contains research articles of the highest quality in all areas of pure and applied mathematics., new characterizations involving Moore determinants, and an application to the Weil pairing on Drinfeld modules. We also deп¬Ѓne Drinfeld modular functions of non-zero type and provide a moduli interpretation of these. 1 Drinfeld modular forms We start with a brief introduction to Drinfeld modular forms, see e.g. [7] for more details..

### AMS Journal of the American Mathematical Society

AN INTRODUCTION TO INVARIANTS AND MODULI. 20-7-2010В В· Denote by P the fractional power of L which is a pseudo-differential operator of the form One main result in the present paper is that the nth series of flows of the DrinfeldвЂ“Sokolov hierarchy of D n type can be represented by the square root of L regarded as an element of For full access to this pdfвЂ¦ https://en.wikipedia.org/wiki/Drinfeld_module 10-6-2014В В· B. Poonen, вЂњFractional power series and pairings on Drinfeld modules,вЂќ Journal of the American Mathematical Society, vol. 9, no. 3, pp. 783вЂ“812, 1996. View at Publisher В· View at Google Scholar В· View at Zentralblatt MATH В· View at MathSciNet В· View at Scopus.

new characterizations involving Moore determinants, and an application to the Weil pairing on Drinfeld modules. We also deп¬Ѓne Drinfeld modular functions of non-zero type and provide a moduli interpretation of these. 1 Drinfeld modular forms We start with a brief introduction to Drinfeld modular forms, see e.g. [7] for more details. Many of these results extend to non-linear fractional power series. We apply these results to construct a Drinfeld module analogue of the Weil pairing, and to describe the topological module structure of the kernel of the adjoint exponential of a Drinfeld module

Zeros of Eisenstein series, quadratic class numbers and supersingularity for rational function elds by Gunther Cornelissen for a given Drinfeld module can be deduced. In the course of the proof, 2-power divisibility of the class number of certain hyperelliptic extensions of F q(T) These invited articles by leading researchers in the field explore various aspects of the parallel worlds of function fields and number fields. Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives.

Journal of Number Theory 142 (2014) 18вЂ“43 Contents lists available at ScienceDirect Journal of Number Theory. www.elsevier.com/locate/jnt. On the trace and norm GossL-functions Peter Bruin Seminar on Drinfeld modules 14 and 21 October 2015 1. Introduction 1.1. Motivation The purpose of this talk is to introduce Goss L-functions.

Past seminars. October 31, 2019 - room SR701 - time: 13:30 - Nahid Walji . Three lectures on Drinfeld modules and Drinfeld modular forms Г la Katz Kummer extensions of rings of formal power series, and perfectoid algebras A survey of Drinfeld modular forms 25.03.97 G. Cornelissen 1 The possibility of a theory of modular forms for function п¬Ѓelds was perhaps implicit in Drin-feldвЂ™s original work, but the notion was only really introduced by Goss and Gekeler in the beginning of the eighties. A lot of it developped along вЂњclassicalвЂќ lines (by the word вЂњclassi-

To be published in the LNM-series of Springer-Verlag. [4] N. Bourbaki. Elements of G.J. van der Heiden. Factoring polynomials over nite elds with Drinfeld modules. To appear in Math Weil pairing for Drinfeld modules. To appear in Monatsh. Math., 2003. Bibliography 139 [30] G.J. van der Heiden. Local-global problem for Drinfeld modules numbers (except the nonpositive integers) by knowing only the value of the gamma function between 1 and 2. Table 2 contains the gamma function for arguments between 1 and 1.99. To illustrate, the following three examples show how to evaluate the gamma function for positive integers, fractional positive numbers and a negative noninteger values.

COLEMANвЂ™S POWER SERIES AND WILESвЂ™ RECIPROCITY FOR RANK 1 DRINFELD MODULES FRANCESC BARS, IGNAZIO LONGHI Abstract. We introduce the formalism of ColemanвЂ™s power series for rank 1 Drinfeld modules and apply it to formulate and prove the analogue of WilesвЂ™ explicit reciprocity law in this setting. 1. Introduction Many of these results extend to non-linear fractional power series. We apply these results to construct a Drinfeld module analogue of the Weil pairing, and to describe the topological module structure of the kernel of the adjoint exponential of a Drinfeld module.

AN INTRODUCTION TO INVARIANTS AND MODULI 41 G. Laumon Cohomology of Drinfeld modular varieties I 42 E.B. Davies Spectral theory and differential operators Power series rings 61 (b) Valuation rings 63 2.5 A diversion: rings of invariants which are not п¬Ѓnitely generated 68 Fractional Power Series and Pairings on Drinfeld Modules Created Date: 20160730200410Z

Fractional Power Series and Pairings on Drinfeld Modules Created Date: 20160730200410Z uniformization of Drinfeld modules and the related analytic functions (section 2) and report on the structure of the ring of modular forms in the classical (section 1) and the Drinfeld case (section 3), and on the role played by the respective Eisenstein series, discriminant, and j-invariant functions. In the fourth section, we give a brief

associated to the Drinfeld A-module r. We show that this module is п¬Ѓnitely generated and consists of the fractional ideals of A relatively prime to m, such that yj A = c. The Goss L-function for y is deп¬Ѓned to be The power series S(tm;z):=exp Past seminars. October 31, 2019 - room SR701 - time: 13:30 - Nahid Walji . Three lectures on Drinfeld modules and Drinfeld modular forms Г la Katz Kummer extensions of rings of formal power series, and perfectoid algebras

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