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QUANTUM UNIQUE ERGODICITY AND NUMBER THEORY
"... In this course I will describe recent progress on the “Quantum Unique Ergodicity ” conjecture of Rudnick and Sarnak in a special arithmetic situation. To explain what this conjecture is about, let H denote the upper half plane {x + iy: y> 0}. The group SL2(R) acts on H by ..."
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In this course I will describe recent progress on the “Quantum Unique Ergodicity ” conjecture of Rudnick and Sarnak in a special arithmetic situation. To explain what this conjecture is about, let H denote the upper half plane {x + iy: y> 0}. The group SL2(R) acts on H by
Singularities, Supersymmetry and Combinatorial Reciprocity
, 2013
"... (Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. ..."
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(Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters.
GALOIS REPRESENTATIONS, AUTOMORPHIC FORMS, AND THE SATOTATE CONJECTURE
"... An elliptic curve is the set E of solutions of a cubic curve in two variables, for example E: y2 + y = x3 + x. I will only consider elliptic curves with rational coefficients, which after a change ..."
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An elliptic curve is the set E of solutions of a cubic curve in two variables, for example E: y2 + y = x3 + x. I will only consider elliptic curves with rational coefficients, which after a change