# 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

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topBlomer, 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 $c>0$ 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 $c>0$ 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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