Automorphic Forms, Representations, and L-Functions: by Armand Borel

By Armand Borel

Comprises sections on Reductive teams, representations, Automorphic kinds and representations

Show description

Read or Download Automorphic Forms, Representations, and L-Functions: Symposium in Pure Mathematics. Volume XXXIII Part 1 PDF

Similar number theory books

Number Theory: Structures, Examples, and Problems

This introductory textbook takes a problem-solving method of quantity concept, situating each one suggestion in the framework of an instance or an issue for fixing. beginning with the necessities, the textual content covers divisibility, special factorization, modular mathematics and the chinese language the rest Theorem, Diophantine equations, binomial coefficients, Fermat and Mersenne primes and different unique numbers, and detailed sequences.

Elementary Number Theory (7th Edition)

Trouble-free quantity concept, 7th version, is written for the one-semester undergraduate quantity concept path taken via math majors, secondary schooling majors, and laptop technology scholars. this modern textual content presents an easy account of classical quantity idea, set opposed to a historic history that exhibits the subject's evolution from antiquity to contemporary learn.

Special Matrices and Their Applications in Numerical Mathematics

This revised and corrected moment version of a vintage ebook on precise matrices offers researchers in numerical linear algebra and scholars of normal computational arithmetic with an important reference. writer Miroslav Fiedler, a Professor on the Institute of desktop technology of the Academy of Sciences of the Czech Republic, Prague, starts with definitions of easy ideas of the idea of matrices and basic theorems.

Lattice Sums Then and Now

The research of lattice sums begun whilst early investigators desired to move from mechanical houses of crystals to the homes of the atoms and ions from which they have been equipped (the literature of Madelung's constant). A parallel literature was once outfitted round the optical homes of normal lattices of atoms (initiated by means of Lord Rayleigh, Lorentz and Lorenz).

Additional info for Automorphic Forms, Representations, and L-Functions: Symposium in Pure Mathematics. Volume XXXIII Part 1

Sample text

Elementary Results PROOF. 1), we find that x 2 - 2xy + 2y2 - Z = o. 3) by 2 and rearranging terms, we arrive at (2y)2 - 2(2y)x + 2X2 - 2z = O. 4). 1). The previous three entries demonstrate Ramanujan's keen eye in spotting beautiful algebraic relationships. Entry 14 (p. 337). 1) where p and q are constants. 2) cp(x) Let Fl be defined by F(x) = Fl(X)X(X). Then F l(X + p) + F l(X + q) = PROOF. 1), we find that F(x + p) F(x + q) F 1(x+p)+F 1(x+q)= ( )+ ( ) xx+p xx+q = + p) + -'----'---'---''------=l/J(x)F(x + q) X(x + p) cp(x)X(x + p) F(x cp(x)F(x + p) + l/J(x)F(x + q) cp(x)X(x + p) f(x) cp(x)x(x + p)' which completes the proof.

328). 1) and a[3 = 1. 2) 24 22. 3) where y and () are positive numbers such that y{) = 1 and 125z y-{)=11+6 • x PROOF. f3 = 1, (1 + ~Y = (1. 1/5 - ((1. - f3) - 5{ (1 = = ((1. 2), + 11 ;6 = (1 + 5f33/5 - f3 +~)} + 10(1 +~) +~). y + ~Y + 5(1 + ~ + 5(1 + ~). 4) Expanding and simplifying, we deduce that z = 25xy 5 + 25x 2y 4 + 15x3 y 3 + 5x4 y2 + x 5 y. This may be rewritten in the form 11 + l~~Z = 11 + C:Y + 5c:r + 15(~y + 25C:Y + 25C:) = (1 + 5:Y + 5(1 + ~y + 5(1 + ~). 5). 1). Entry 13 (p. 328). 2) 25 22.

N aj - bnj+ 1 ) 1 ,-1 j=o ... b 1, a 1 ••• a,-l a 1 ••• aj )n. 1) Observe that the introduction of the parameter n is adventitious. We thus will assume without loss of generality that n = 1. There are two misprints in Ramanujan's formulation. PROOF. Induct on r. 1) is trivial. 1) holds. Then by induction, if a, #- 0, which completes the proof. Entry 27 (p. 356). 3) are the roots of the equation Z3 PROOF. 4) 0. 3) is apparent. 5) 38 22. Elementary Results and x2 Set x +y= - + xy + y2 + a + 1 = o.

Download PDF sample

Rated 4.04 of 5 – based on 43 votes