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1.
In the mid-1980s an equivalence was established between the simple closed geodesics on the Riemann surfaces obtained as quotients of the upper half plane H by any of the following subgroups of the modular group (1) : , (3), and 3. An axis of a hyperbolic element of (1) projects to a simple closed geodesic on one of these surfaces if and only if it does so on the other two.This equivalence was used to obtain a variety of Diophantine and geometric results. In subsequent related investigations, the role of (1) was assumed by the Hecke triangle group Gq for q 3. (For q = 3, we have (1) = G3.) These works employed the analog of 3, denoted q.In the context of the Gq, the present paper gives the analog of , which we denote q. As in the case q = 3, we have [q:q] = 2. A rather full discussion of geometry of q\ H is given. In particular, we demonstrate that the equivalence of simple closed geodesics on q\ H and q\ H does not hold for q 7.As of this writing, we have not been able to obtain an appropriate analog of (3). 相似文献
2.
— , B
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3.
(L
1,H) (, ) , ; H — . , , L
1 . [13] , . , , , . 相似文献
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ERNST-ULRICH GEKELER 《Compositio Mathematica》1997,106(2):181-202
The discriminant function is a certain rigid analytic modularform defined on Drinfelds upper half-plane . Its absolutevalue may be considered as a function on theassociated Bruhat–Tits tree T. We compare log with the conditionally convergent complex-valued Eisenstein series Edefined on T and thereby obtain results about the growth of and of some related modular forms. We further determine to what extent roots may be extracted of (z)/(nz),regarded as a holomorphic function on . In some cases, this enables us to calculate cuspidal divisor class groups of modular curves. 相似文献
7.
S. I. Novikov 《Analysis Mathematica》1992,18(1):73-86
n
(D) — ,s —
n
(D),
v
(v=1, 2, ...,s/2) — .
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.
The author expresses his gratitude to Yu. N. Subbotin for a useful discussion on the results of this paper. 相似文献
The author expresses his gratitude to Yu. N. Subbotin for a useful discussion on the results of this paper. 相似文献
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Ch. Pommerenke 《Analysis Mathematica》1977,3(4):291-297
f . , , — , A f f(). , , f() 0 . , , ,A , f . , f() - f() . , , . (1976) ( ¦f(z)¦<1) . . (1969) ( ). 相似文献
11.
G. E. Tkebuchava 《Analysis Mathematica》1994,20(2):147-153
. : [0, +) [0, +) - , u+ (u) (u)=o(u lnu). [0, 1]2 f , ¦f¦ L([0, 1]2), - [0, 1]2. 相似文献
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13.
F. Schipp 《Analysis Mathematica》1976,2(2):149-154
. . . . : {ja
j
},j=1,2,... — ,
f(x) ,
, f
[1](x) — f . 相似文献
14.
J. Mogyoródi 《Analysis Mathematica》1981,7(3):185-197
, , . . . [1], , . , , ., , L logL. , , . . . . [5]. , . 相似文献
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R. J. Bagby 《Analysis Mathematica》1982,8(1):3-8
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m
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m
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p
(R
m) x y, Lq(Rn). ׃
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, , , q r . , ( ¦¦) K
0
(y); p, g r , K
0. 相似文献
19.
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n. , , , F R
n, F , R
n R
n .
p,q
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p,q
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d,F— « » F— R
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This work has been supported in part by the Swedish Natural Science Research Council. 相似文献
This work has been supported in part by the Swedish Natural Science Research Council. 相似文献
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