# Bernoulli numbers, Hurwitz numbers, p-adic L-functions and Kummer's criterion.

RACSAM (2007)

- Volume: 101, Issue: 1, page 1-32
- ISSN: 1578-7303

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topLozano Robledo, Alvaro. "Bernoulli numbers, Hurwitz numbers, p-adic L-functions and Kummer's criterion.." RACSAM 101.1 (2007): 1-32. <http://eudml.org/doc/41658>.

@article{LozanoRobledo2007,

abstract = {Let K = Q(ζp) and let hp be its class number. Kummer showed that p divides hp if and only if p divides the numerator of some Bernoulli number. In this expository note we discuss the generalizations of this type of criterion to totally real fields and quadratic imaginary fields.},

author = {Lozano Robledo, Alvaro},

journal = {RACSAM},

keywords = {class numbers; Bernoulli numbers; cyclotomic fields; quadratic fields; -adic -functions; Fermat's equation; elliptic curves; Hurwitz numbers; research exposition},

language = {eng},

number = {1},

pages = {1-32},

title = {Bernoulli numbers, Hurwitz numbers, p-adic L-functions and Kummer's criterion.},

url = {http://eudml.org/doc/41658},

volume = {101},

year = {2007},

}

TY - JOUR

AU - Lozano Robledo, Alvaro

TI - Bernoulli numbers, Hurwitz numbers, p-adic L-functions and Kummer's criterion.

JO - RACSAM

PY - 2007

VL - 101

IS - 1

SP - 1

EP - 32

AB - Let K = Q(ζp) and let hp be its class number. Kummer showed that p divides hp if and only if p divides the numerator of some Bernoulli number. In this expository note we discuss the generalizations of this type of criterion to totally real fields and quadratic imaginary fields.

LA - eng

KW - class numbers; Bernoulli numbers; cyclotomic fields; quadratic fields; -adic -functions; Fermat's equation; elliptic curves; Hurwitz numbers; research exposition

UR - http://eudml.org/doc/41658

ER -

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