4 Graphics Drawing a function of one or two variables, or a series of data, makes it easier to grasp a mathematical or physical phenomenon, and helps us make conjectures. In this chapter, we illustrate the graphical cap

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Galois Representations R. Taylor∗ Abstract In the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations

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On the bicycle transformation and the filament equation: results and conjectures Serge Tabachnikov∗ 1

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TWO HUNDRED AND THIRTEEN CONJECTURES ON PRIMES (COLLECTED PAPERS) Education Publishing 2015

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Some Conjectures about the Impact of Printing on Western Society and Thought: A Preliminary Report Author(s): Elizabeth L. Eisenstein Source: The Journal of Modern History, Vol. 40, No. 1 (Mar., 1968), ppPublished

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WEBER’S CLASS NUMBER PROBLEM TAKASHI FUKUDA AND KEIICHI KOMATSU 1. Introduction Two hundred years ago, Gauss gave the following two conjectures (cf. [2]): Conjecture 1. The imaginary quadratic fields with class number

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arXiv:math/0702460v2 [math.KT] 9 MayInheritance of Isomorphism Conjectures under colimits Arthur Bartels, Siegfried Echterhoff and Wolfgang L¨ uck

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APPEARED IN BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Volume 31, Number 1, July 1994, Pages 1-14 SELBERG’S CONJECTURES AND ARTIN L-FUNCTIONS

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• Algebra
• Abstract algebra
• Mathematics
• Conjectures
• Automorphic forms
• Class field theory
• Representation theory of Lie groups
• Algebraic number theory
• Artin L-function
• Selberg class
• Langlands program
• RamanujanPetersson conjecture

Introduction The present work grew out of an entirely unsuccessful attempt to answer some basic questions about elliptic curves over $. Start with an elliptic curve E over $, say given by a Weierstrass equation E: y2 = 4

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• Mathematics
• Analytic number theory
• Number theory
• Mathematical analysis
• Elliptic curves
• Conjectures
• Diophantine geometry
• Millennium Prize Problems
• Birch and Swinnerton-Dyer conjecture
• Rank of an elliptic curve
• Modular form
• Riemann hypothesis

Lifting Galois covers of algebraic curves Frans Oort Intercity number theory seminar, Utrecht, June 8, 2012. Introduction

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• Algebraic geometry
• Geometry
• Algebra
• Algebraic curves
• Niels Henrik Abel
• Algebraic surfaces
• Abelian variety
• Abelian group
• tale fundamental group
• Conjectures
• Curve
• ArtinSchreier curve