Optimization of Electrical Production The production of electricity in France is optimized everyday with the help of a mathematical software developed at Inria, in collaboration with EDF R&D. Substantial performance is a

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The Mandelbrot Set as a Modular Form Linas Vepstas 2 January 2005 (revised 30 May 2005) Abstract An exploration of the interior or the Mandelbrot Set and the appearance of functions appearing to be simi

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• Analytic number theory
• Mathematical series
• Complex dynamics
• Calculus
• Mandelbrot set
• Series
• Modular form
• Summation
• Elliptic curve
• Mathematical analysis
• Mathematics
• Fractals

Automorphic forms on Os+2,2 (R)+ and generalized Kac-Moody algebras. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Z¨ urich, 1994), 744–752, Birkh¨auser, Basel, 1995. Richard E. Borcherds *

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• Lie algebras
• Modular forms
• Elliptic functions
• Moonshine theory
• Q-analogs
• J-invariant
• Monster Lie algebra
• Generalized Kac–Moody algebra
• Representation theory
• Abstract algebra
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MATHEMATICS OF COMPUTATION Volume 71, Number 240, Pages 1803–1806 S[removed][removed]Article electronically published on May 28, 2002 CORRIGENDUM TO “PERIOD OF THE POWER GENERATOR

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• Divisor function
• Carmichael function
• Elliptic functions
• Modular forms
• Arithmetic function
• Spectral theory of ordinary differential equations
• Mathematics
• Modular arithmetic
• Number theory

Reflection groups of Lorentzian lattices. 21 September[removed]Duke Math. J[removed]no. 2, [removed]Richard E. Borcherds, ∗

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• Modular forms
• Elliptic functions
• Riemann surfaces
• Lie groups
• Analytic number theory
• Lattice
• Theta function
• Möbius transformation
• Unimodular lattice
• Mathematical analysis
• Abstract algebra
• Geometry

Automorphic forms with singularities on Grassmannians. 29 September 1996, corrected 29 May[removed]Richard E. Borcherds,∗ D.P.M.M.S., 16 Mill Lane, Cambridge, CB2 1SB, England. e-mail: [removed] home page: http

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• Abstract algebra
• Analytic number theory
• Elliptic functions
• Q-analogs
• Theta function
• Eisenstein series
• J-invariant
• Metaplectic group
• Rankin–Selberg method
• Mathematical analysis
• Modular forms
• Mathematics

MODULAR CURVES AND RAMANUJAN’S CONTINUED FRACTION BRYDEN CAIS AND BRIAN CONRAD Abstract. We use arithmetic models of modular curves to establish some properties of Ramanujan’s continued fraction. In particular, we gi

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• Modular forms
• Analytic number theory
• Elliptic functions
• Riemann surfaces
• Algebraic curves
• J-invariant
• Theta function
• Congruence subgroup
• Classical modular curve
• Abstract algebra
• Mathematical analysis
• Mathematics

2014 ARIZONA WINTER SCHOOL: ARITHMETIC STATISTICS STATISTICS FOR ZEROES OF L-FUNCTIONS OF CURVES OVER FINITE FIELDS CHANTAL DAVID The lectures will be concerned with statistics for the zeroes of L-functions in natural fa

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• Algebraic number theory
• Field theory
• Hyperelliptic curve
• Peter Sarnak
• Elliptic curve
• Zeta function
• L-function
• Algebraic number field
• Abstract algebra
• Algebraic curves
• Analytic number theory

CURVES AND ZETA FUNCTIONS OVER FINITE FIELDS POSSIBLE PROJECTS CHANTAL DAVID, CONCORDIA UNIVERSITY ASSISTANT: ALINA BUCUR, UCSD For background material, and more details about the projects, see the notes.

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• Algebra
• Hyperelliptic curve
• Moduli space
• Elliptic curve
• Gonality of an algebraic curve
• Artin–Schreier theory
• L-function
• Zeta function
• Curve
• Abstract algebra
• Algebraic curves
• Geometry

CURVES AND ZETA FUNCTIONS OVER FINITE FIELDS ARIZONA WINTER SCHOOL 2014: ARITHMETIC STATISTICS CHANTAL DAVID ASSISTANT: ALINA BUCUR 1. Introduction

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• Analytic number theory
• Fourier analysis
• Conjectures
• Meromorphic functions
• Riemann hypothesis
• Riemann zeta function
• Elliptic curve
• Dirac delta function
• Algebraic number field
• Mathematical analysis
• Mathematics
• Abstract algebra