Generalised Dirichlet series and Hecke's functional equation
نویسندگان
چکیده
منابع مشابه
On a functional equation satisfied by certain Dirichlet series
by giving a representation of L(s) in terms of Hurwitz zeta functions. That representation allowed us to get some information about zeros and poles; nevertheless no functional equation could be deduced from it. In this paper following a classical argument we obtain for L(s) as above, under suitable hypothesis, a functional equation of Riemann’s type. More precisely, let us consider the Dirichle...
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This definition could have been given to an 18th or early 19th century mathematical audience, but it would not have been very popular: probably they would not have been comfortable with the Humpty Dumpty-esque redefinition of multiplication. Mathematics at that time did have commutative rings: rings of numbers, of matrices, of functions, but not rings with a “funny” multiplication operation def...
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where the an are complex numbers and s is a complex variable. Such functions are called Dirichlet series. We call a1 the constant term. A Dirichlet series will often be written as ∑ ann −s, with the index of summation understood to start at n = 1. Similarly, ∑ app −s runs over the primes, and ∑ apkp −ks runs over the prime powers excluding 1. (Not counting 1 as a prime power in that notation is...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1967
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500011962