Arithmetic statistics of modular symbols
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Standard
Arithmetic statistics of modular symbols. / Petridis, Yiannis N.; Risager, Morten S.
I: Inventiones Mathematicae, Bind 212, Nr. 3, 06.2018, s. 997-1053.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - Arithmetic statistics of modular symbols
AU - Petridis, Yiannis N.
AU - Risager, Morten S.
PY - 2018/6
Y1 - 2018/6
N2 - Mazur, Rubin, and Stein have recently formulated a series of conjecturesabout statistical properties of modular symbols in order to understandcentral values of twists of elliptic curve L-functions. Two of these conjecturesrelate to the asymptotic growth of the first and second moments of the modularsymbols. We prove these on average by using analytic properties of Eisensteinseries twisted by modular symbols. Another of their conjectures predicts theGaussian distribution of normalized modular symbols ordered according tothe size of the denominator of the cusps. We prove this conjecture in a refinedversion that also allows restrictions on the location of the cusps.
AB - Mazur, Rubin, and Stein have recently formulated a series of conjecturesabout statistical properties of modular symbols in order to understandcentral values of twists of elliptic curve L-functions. Two of these conjecturesrelate to the asymptotic growth of the first and second moments of the modularsymbols. We prove these on average by using analytic properties of Eisensteinseries twisted by modular symbols. Another of their conjectures predicts theGaussian distribution of normalized modular symbols ordered according tothe size of the denominator of the cusps. We prove this conjecture in a refinedversion that also allows restrictions on the location of the cusps.
U2 - 10.1007/s00222-017-0784-7
DO - 10.1007/s00222-017-0784-7
M3 - Journal article
VL - 212
SP - 997
EP - 1053
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
SN - 0020-9910
IS - 3
ER -
ID: 200291620