Functional equations of p-adic L-functions at supersingular primes imply a relation between leading and sub-leading terms, parity of vanishing orders, and invariance of Iwasawa invariants under conjugate twists.
The Šafarevič-Tate group in cyclotomic Zp-extensions at supersingular primes
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Consequences of functional equations for pairs of p-adic L-functions
Functional equations of p-adic L-functions at supersingular primes imply a relation between leading and sub-leading terms, parity of vanishing orders, and invariance of Iwasawa invariants under conjugate twists.