Zeta functions do not determine class numbers
نویسندگان
چکیده
منابع مشابه
Transcendental Numbers and Zeta Functions
The concept of “number” has formed the basis of civilzation since time immemorial. Looking back from our vantage point of the digital age, we can agree with Pythagoras that “all is number”. The study of numbers and their properties is the mathematical equivalent of the study of atoms and their structure. It is in fact more than that. The famous physicist and Nobel Laureate Eugene Wigner spoke o...
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Let F ′/F be a finite normal extension of number fields with Galois group Gal(F ′/F ). Let χ be an irreducible character of Gal(F ′/F ) of degree greater than one and L(s, χ) the associated Artin L-function. Assuming the truth of Artin’s conjecture, we have explicitly determined a zero-free region about 1 for L(s, χ). As an application we show that, for a CM-field K of degree 2n with solvable n...
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The incomplete gamma function expansion for the perturbed Epstein zeta function is known as Ewald expansion. In this paper we state a special case of the main formula in Kanemitsu and Tsukada (Contributions to the theory of zeta-functions: the modular relation supremacy. World Scientific, Singapore, 2014) whose specifications will give Ewald expansions in the H-function hierarchy. An Ewald expa...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1994
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1994-00520-8