Natural boundaries for Euler products of Igusa zeta functions of elliptic curves
2018 ◽
Vol 14
(08)
◽
pp. 2317-2331
Keyword(s):
We study the analytic behavior of adelic versions of Igusa integrals given by integer polynomials defining elliptic curves. By applying results on the meromorphic continuation of symmetric power L-functions and the Sato–Tate conjectures, we prove that these global Igusa zeta functions have some meromorphic continuation until a natural boundary beyond which no continuation is possible.
1977 ◽
Vol 29
(6)
◽
pp. 1292-1299
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Keyword(s):
2004 ◽
Vol 15
(07)
◽
pp. 691-715
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Keyword(s):
1986 ◽
Vol 62
(5)
◽
pp. 193-196
2020 ◽
Vol 117
(9)
◽
pp. 4546-4558
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Keyword(s):