162:
54:
243:
220:
29:
25:
260:
21:
195:
157:{\displaystyle \Theta _{L}^{g}(T)=\sum _{\lambda \in L^{g}}\exp(\pi iTr(\lambda T\lambda ^{t}))}
237:
216:
230:
226:
215:, Grundlehren der Mathematischen Wissenschaften, vol. 254. Springer-Verlag, Berlin,
254:
201:
When the degree is 1 this is just the usual theta function of a lattice.
187:
198:
then this is a Siegel modular form for the full Siegel modular group.
44:
is a positive definite lattice. The Siegel theta series of degree
171:
is an element of the Siegel upper half plane of degree
57:
156:
8:
190:of the Siegel modular group. If the lattice
242:: CS1 maint: location missing publisher (
142:
100:
89:
67:
62:
56:
178:This is a Siegel modular form of degree
235:
7:
59:
24:associated to a positive definite
14:
151:
148:
129:
114:
79:
73:
28:, generalizing the 1-variable
1:
30:theta function of a lattice
277:
213:Siegelsche Modulfunktionen
158:
159:
211:Freitag, E. (1983),
55:
72:
22:Siegel modular form
18:Siegel theta series
154:
107:
58:
16:In mathematics, a
261:Automorphic forms
85:
268:
247:
241:
233:
163:
161:
160:
155:
147:
146:
106:
105:
104:
71:
66:
276:
275:
271:
270:
269:
267:
266:
265:
251:
250:
234:
223:
210:
207:
182:and weight dim(
138:
96:
53:
52:
48:is defined by
38:
12:
11:
5:
274:
272:
264:
263:
253:
252:
249:
248:
221:
206:
203:
165:
164:
153:
150:
145:
141:
137:
134:
131:
128:
125:
122:
119:
116:
113:
110:
103:
99:
95:
92:
88:
84:
81:
78:
75:
70:
65:
61:
37:
34:
13:
10:
9:
6:
4:
3:
2:
273:
262:
259:
258:
256:
245:
239:
232:
228:
224:
222:3-540-11661-3
218:
214:
209:
208:
204:
202:
199:
197:
193:
189:
186:)/2 for some
185:
181:
176:
174:
170:
143:
139:
135:
132:
126:
123:
120:
117:
111:
108:
101:
97:
93:
90:
86:
82:
76:
68:
63:
51:
50:
49:
47:
43:
40:Suppose that
35:
33:
31:
27:
23:
19:
212:
200:
194:is even and
191:
183:
179:
177:
172:
168:
166:
45:
41:
39:
17:
15:
205:References
196:unimodular
36:Definition
140:λ
133:λ
118:π
112:
94:∈
91:λ
87:∑
60:Θ
255:Category
238:citation
188:subgroup
231:0871067
26:lattice
229:
219:
167:where
20:is a
244:link
217:ISBN
109:exp
257::
240:}}
236:{{
227:MR
225:,
175:.
32:.
246:)
192:L
184:L
180:d
173:g
169:T
152:)
149:)
144:t
136:T
130:(
127:r
124:T
121:i
115:(
102:g
98:L
83:=
80:)
77:T
74:(
69:g
64:L
46:g
42:L
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