Displaying similar documents to “Erratum : “ C - -Whittaker vectors for complex semisimple Lie groups, wave front sets, and Goldie rank polynomial representations””

On blocks of arithmetic progressions with equal products

N. Saradha (1997)

Journal de théorie des nombres de Bordeaux

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Let f ( X ) [ X ] be a monic polynomial which is a power of a polynomial g ( X ) [ X ] of degree μ 2 and having simple real roots. For given positive integers d 1 , d 2 , , m with < m and gcd ( , m ) = 1 with μ m + 1 whenever m < 2 , we show that the equation f ( x ) f ( x + d 1 ) f ( x + ( k - 1 ) d 1 ) = f ( y ) f ( y + d 2 ) f ( y + ( m k - 1 ) d 2 ) with f ( x + j d 1 ) 0 for 0 j < k has only finitely many solutions in integers x , y and k 1 except in the case m = μ = 2 , = k = d 2 = 1 , f ( X ) = g ( X ) , x = f ( y ) + y .

Topological properties of two-dimensional number systems

Shigeki Akiyama, Jörg M. Thuswaldner (2000)

Journal de théorie des nombres de Bordeaux

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In the two dimensional real vector space 2 one can define analogs of the well-known q -adic number systems. In these number systems a matrix M plays the role of the base number q . In the present paper we study the so-called fundamental domain of such number systems. This is the set of all elements of 2 having zero integer part in their “ M -adic” representation. It was proved by Kátai and Környei, that is a compact set and certain translates of it form a tiling of the 2 . We construct...