Non-vanishing of class group L -functions at the central point

Valentin Blomer[1]

  • [1] University of Toronto, Department of Mathematics, 100 St. George Street, Toronto M5S 3G3, Ontario, (Canada)

Annales de l’institut Fourier (2004)

  • Volume: 54, Issue: 4, page 831-847
  • ISSN: 0373-0956

Abstract

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Let K = ℚ ( - D ) be an imaginary quadratic field, and denote by h its class number. It is shown that there is an absolute constant c > 0 such that for sufficiently large D at least c · h ∏ p ∣ D ( 1 - p - 1 ) of the h distinct L -functions L K ( s , χ ) do not vanish at the central point s = 1 / 2 .

How to cite

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Blomer, Valentin. "Non-vanishing of class group $L$-functions at the central point." Annales de l’institut Fourier 54.4 (2004): 831-847. <http://eudml.org/doc/116134>.

@article{Blomer2004,
abstract = {Let $K = \{\mathbb \{Q\}\}(\sqrt\{-D\})$ be an imaginary quadratic field, and denote by $h$ its class number. It is shown that there is an absolute constant $c&gt;0$ such that for sufficiently large $D$ at least $c \cdot h \prod _\{p \mid D\} (1-p^\{-1\})$ of the $h$ distinct $L$-functions $L_K(s, \chi )$ do not vanish at the central point $s = 1/2$.},
affiliation = {University of Toronto, Department of Mathematics, 100 St. George Street, Toronto M5S 3G3, Ontario, (Canada)},
author = {Blomer, Valentin},
journal = {Annales de l’institut Fourier},
keywords = {non-vanishing results; $L$-functions; imaginary quadratic fields; mollifier; -functions},
language = {eng},
number = {4},
pages = {831-847},
publisher = {Association des Annales de l'Institut Fourier},
title = {Non-vanishing of class group $L$-functions at the central point},
url = {http://eudml.org/doc/116134},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Blomer, Valentin
TI - Non-vanishing of class group $L$-functions at the central point
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 4
SP - 831
EP - 847
AB - Let $K = {\mathbb {Q}}(\sqrt{-D})$ be an imaginary quadratic field, and denote by $h$ its class number. It is shown that there is an absolute constant $c&gt;0$ such that for sufficiently large $D$ at least $c \cdot h \prod _{p \mid D} (1-p^{-1})$ of the $h$ distinct $L$-functions $L_K(s, \chi )$ do not vanish at the central point $s = 1/2$.
LA - eng
KW - non-vanishing results; $L$-functions; imaginary quadratic fields; mollifier; -functions
UR - http://eudml.org/doc/116134
ER -

References

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