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Siegel theta series

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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.
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is a positive definite lattice. The Siegel theta series of degree
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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

Index

Siegel modular form
lattice
theta function of a lattice
subgroup
unimodular
ISBN
3-540-11661-3
MR
0871067
citation
link
Category
Automorphic forms

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