On x³ + y³ + z³ = 3μxyz and Jacobi polynomials
On special values of generalized p-adic hypergeometric functions
Dedekind sums with characters and class numbers of imaginary quadratic fields
Indices of subfields of cyclotomic ℤₚ-extensions and higher degree Fermat quotients
We consider the indices of subfields of cyclotomic ℤₚ-extensions of number fields. For the nth layer Kₙ of the cyclotomic ℤₚ-extension of ℚ, we find that the prime factors of the index of Kₙ/ℚ are those primes less than the extension degree pⁿ which split completely in Kₙ. Namely, the prime factor q satisfies , and this leads us to consider higher degree Fermat quotients. Indices of subfields of cyclotomic ℤₚ-extensions of a number field which is cyclic over ℚ with extension degree a prime different...
Generalizations of Dedekind sums and their reciprocity laws
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