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Distribution of values of Hecke characters of infinite order

C. S. Rajan (1998)

Acta Arithmetica

We show that the number of primes of a number field K of norm at most x, at which the local component of an idele class character of infinite order is principal, is bounded by O(x exp(-c√(log x))) as x → ∞, for some absolute constant c > 0 depending only on K.

Extension of Estermann’s theorem to Euler products associated to a multivariate polynomial

Ludovic Delabarre (2013)

Bulletin de la Société Mathématique de France

Given a multivariate polynomial h X 1 , , X n with integral coefficients verifying an hypothesis of analytic regularity (and satisfying h ( 0 ) = 1 ), we determine the maximal domain of meromorphy of the Euler product p prime h p - s 1 , , p - s n and the natural boundary is precisely described when it exists. In this way we extend a well known result for one variable polynomials due to Estermann from 1928. As an application, we calculate the natural boundary of the multivariate Euler products associated to a family of toric varieties.

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