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Displaying similar documents to “Diagonal equations over p-adic fields”

Linear independence of values of a certain generalisation of the exponential function – a new proof of a theorem of Carlson

Rolf Wallisser (2005)

Journal de Théorie des Nombres de Bordeaux

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Let Q be a nonconstant polynomial with integer coefficients and without zeros at the non–negative integers. Essentially with the method of Hermite, a new proof is given on linear independence of values at rational points of the function G ( x ) = ∑ n = 0 ∞ x n Q ( 1 ) Q ( 2 ) ⋯ Q ( n ) .

On the power-series expansion of a rational function

D. V. Lee (1992)

Acta Arithmetica

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Introduction. The problem of determining the formula for P S ( n ) , the number of partitions of an integer into elements of a finite set S, that is, the number of solutions in non-negative integers, h s ₁ , . . . , h s k , of the equation hs₁ s₁ + ... + hsk sk = n, was solved in the nineteenth century (see Sylvester [4] and Glaisher [3] for detailed accounts). The solution is the coefficient of x ⁿ i n [(1-xs₁)... (1-xsk)]-1, expressions for which they derived. Wright [5] indicated a simpler method by which to find part...