STRUCTURE AND RANDOMNESS IN THE PRIME NUMBERS TERENCE TAO Abstract. A quick tour through some topics in analytic prime number theory.

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Combinatorial and Analytic Number Theory Course fall 2007 R. Tijdeman December 21, 2007 2

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On transcendental number theory, classical analytic functions and Diophantine geometry B. Zilber University of Oxford

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Research Statement: Steven J Miller November 16, 2010 My main interest is analytic number theory and random matrix theory (especially the distribution of zeros of 𝐿-functions and the eigen

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NEKST VOL. 23 NO. 4 Summer 2015 NEKST-ONLINE.NL

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• Mathematical analysis
• Complex analysis
• Mathematics
• Analytic number theory
• Bernhard Riemann
• Riemann zeta function
• Zeta
• Special functions
• Real analytic Eisenstein series
• Table of stars with Bayer designations

On polynomials attached to curves F. Morain Laboratoire d’Informatique de l’École polytechnique logoUW ECOL E

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• Mathematical analysis
• Mathematics
• Special functions
• Analytic number theory
• Elliptic curve
• Group theory
• Analytic functions
• Orthogonal polynomials
• Barnes G-function

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

425 Documenta Math. Volumes of Symmetric Spaces via Lattice Points Henri Gillet and Daniel R. Grayson

Source URL: documenta.sagemath.org

• Mathematics
• Abstract algebra
• Algebra
• Analytic number theory
• Bernhard Riemann
• Riemann zeta function
• Lattice

125 Documenta Math. Lifting from two Elliptic Modular Forms to Siegel Modular Forms of Half-Integral Weight

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• Mathematical analysis
• Mathematics
• Modular forms
• Algebra
• Automorphic forms
• Analytic number theory
• Linear algebra
• Eisenstein series
• Theta constant
• Hecke operator
• Siegel modular form
• Jacobi form

ON A PROPERNESS OF THE HILBERT EIGENVARIETY AT INTEGRAL WEIGHTS: THE CASE OF QUADRATIC RESIDUE FIELDS SHIN HATTORI Abstract. Let p be a rational prime. Let F be a totally real number field such that F is unramified over

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• Algebra
• Mathematics
• Abstract algebra
• Modular forms
• Field theory
• Analytic number theory
• Operator theory
• Algebraic geometry
• Eigenform
• P-adic modular form
• Elliptic curve
• Valuation