Заглавие | RIEMANN HYPOTHESIS ANALOGUE FOR LOCALLY FINITE MODULES OVER THE ABSOLUTE GALOIS GROUP OF A FINITE FIELD |
Вид публикация | Journal Article |
Година на публикуване | 2017 |
Автори | Kasparian A, Marinov I |
Списание | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |
Том | 104 |
Pagination | 99-137 |
ISSN | 0205-0808 |
ключови думи | $\zeta$-function of a locally finite $\mathfrak{G}$-module; Riemann Hypothesis Analogue with respect to the projective line; finite unramified coverings of locally finite $\mathfrak{G}$-modules with Galois closure. |
Резюме | The article provides a sufficient condition for a locally finite module $M$ over the absolute Galois group $\mathfrak{G} = Gal(\overline{\mathbb{F}_q}/\mathbb{F}_q)$ of a finite field $\mathbb{F}_q$ to satisfy the Riemann Hypothesis Analogue with respect to the projective line $\mathbb{P}^1(\overline{\mathbb{F}_q})$. The condition holds for all smooth irreducible projective curves of positive genus, defined over $\mathbb{F}_q$. We give an explicit example of a locally finite module, subject to the assumptions of our main theorem and, therefore, satisfying the Riemann Hypothesis Analogue with respect to $\mathbb{P}^1(\overline{\mathbb{F}_q})$, which is not isomorphic to a smooth irreducible projective curve, defined over $\mathbb{F}_q$. |
2000 MSC | 14G15, 94B27, 11M38 |
Прикачен файл | Размер |
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104-099-137.pdf | 429.57 KB |