/LastChar 196 (The Poisson Summation Formula, Theta Functions, and the Zeta Function) endobj /Widths[342.6 581 937.5 562.5 937.5 875 312.5 437.5 437.5 562.5 875 312.5 375 312.5 << /S /GoTo /D (section.5.5) >> << << /S /GoTo /D (section.4.3) >> endobj 777.8 777.8 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 15 0 obj 511.1 511.1 511.1 831.3 460 536.7 715.6 715.6 511.1 882.8 985 766.7 255.6 511.1] 4�&,�lp�h�~2&NM�ʴ#��A/_�+,,*����*��}O��H�%Q��;s�Yo� Dݷ�9�
[�QX�,���.=�(%ٕ���8�J��B-HQD�"�" \��P��i>�e�b���U|��tf����6w�DV���U'G�������ʃ~��������!����!�^d���P��Q`~��|�+R����L�N(��H�m0�ͦ�������c� ��H��?Aw작�d���G
æ�ߪ��Ӥ�i����8��ʔLʖI�F�zy����>�!z|�x�iaY���8
~��%Y ��y
S�}Wۻ�|@FӶ�#��\��!�9��Ѥbѫ� ,h� 143 0 obj 766.7 715.6 766.7 0 0 715.6 613.3 562.2 587.8 881.7 894.4 306.7 332.2 511.1 511.1 endobj 306.7 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 306.7 306.7 (Fourier analysis on Z*\(q\)) 19 0 obj 750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 /FirstChar 33 (Fourier analysis on Z\(N\)) 275 1000 666.7 666.7 888.9 888.9 0 0 555.6 555.6 666.7 500 722.2 722.2 777.8 777.8 147 0 obj endobj 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 643.8 839.5 787 710.5 682.1 763 734.6 787 734.6 endobj 7 0 obj x�3PHW0Pp�2@��B���,,�,͌�B���
���,M�,-BR�5�4cC��Z\C� _�� 11 0 obj endobj endobj >> 99 0 obj << /S /GoTo /D (section.3.1) >> endobj 136 0 obj << /S /GoTo /D (section.6.6) >> endobj /Type /Page 24 0 obj 107 0 obj 116 0 obj 194 0 obj endobj endobj /Type/Font /BaseFont/MCADNU+CMR10 128 0 obj endobj endobj 314.8 524.7 524.7 524.7 524.7 524.7 524.7 524.7 524.7 524.7 524.7 524.7 314.8 314.8 850.9 472.2 550.9 734.6 734.6 524.7 906.2 1011.1 787 262.3 524.7] endobj 812.5 875 562.5 1018.5 1143.5 875 312.5 562.5] << /S /GoTo /D (section.5.1) >> << /S /GoTo /D (section.6.2) >> Fourier analysis is the study of how general functions can be decomposed into trigonometric or exponential functions with deflnite frequencies. endobj 180 0 obj (The wave equation in d=1) /Name/F3 /Type/Font (Three dimensions) %PDF-1.2 �hw�q���//�~�w* 285.5 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 285.5 285.5 endobj (Introduction) 742.3 799.4 0 0 742.3 599.5 571 571 856.5 856.5 285.5 314 513.9 513.9 513.9 513.9 endobj 189 0 obj 542.4 542.4 456.8 513.9 1027.8 513.9 513.9 513.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 179 0 obj /ColorSpace 3 0 R /Pattern 2 0 R /ExtGState 1 0 R 770.7 628.1 285.5 513.9 285.5 513.9 285.5 285.5 513.9 571 456.8 571 457.2 314 513.9 /ColorSpace 3 0 R /Pattern 2 0 R /ExtGState 1 0 R /LastChar 196 /Name/F5 (Distributions: examples) 473.8 498.5 419.8 524.7 1049.4 524.7 524.7 524.7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 43 0 obj >> 112 0 obj /D [194 0 R /XYZ 159.667 699.082 null] /ProcSet [ /PDF /Text ] << endobj 187 0 obj >> 103 0 obj 127 0 obj endobj 230 0 obj << /S /GoTo /D (section.6.5) >> /LastChar 196 endobj << /S /GoTo /D (section.4.1) >> 875 531.3 531.3 875 849.5 799.8 812.5 862.3 738.4 707.2 884.3 879.6 419 581 880.8 endobj << /S /GoTo /D (section.2.3) >> (Fourier series for d>1) /Subtype/Type1 /FirstChar 33 15 0 obj /Widths[306.7 514.4 817.8 769.1 817.8 766.7 306.7 408.9 408.9 511.1 766.7 306.7 357.8 39 0 obj << (The group Z\(N\)) 777.8 694.4 666.7 750 722.2 777.8 722.2 777.8 0 0 722.2 583.3 555.6 555.6 833.3 833.3 193 0 obj endobj 820.5 796.1 695.6 816.7 847.5 605.6 544.6 625.8 612.8 987.8 713.3 668.3 724.7 666.7 799.2 642.3 942 770.7 799.4 699.4 799.4 756.5 571 742.3 770.7 770.7 1056.2 770.7 /BaseFont/LDNSRQ+CMTI9 endobj endobj endstream << /S /GoTo /D (subsection.2.1.2) >> %���� (Wave Equations) 115 0 obj /Length 283 endobj (Introduction) 571 285.5 314 542.4 285.5 856.5 571 513.9 571 542.4 402 405.4 399.7 571 542.4 742.3 << /S /GoTo /D (section.1.1) >> (Theta functions) 314.8 472.2 262.3 839.5 577.2 524.7 524.7 472.2 432.9 419.8 341.1 550.9 472.2 682.1 endobj /Subtype/Type1 76 0 obj << << /S /GoTo /D (section.1.2) >> 84 0 obj 12 0 obj (The Jacobi theta function) /Parent 192 0 R endobj 59 0 obj stream << /S /GoTo /D (subsection.3.4.1) >> << /FontDescriptor 8 0 R /Type/Font endobj /FontDescriptor 20 0 R << /S /GoTo /D (subsection.2.3.3) >> (The derivative) (The Fourier transform of a distribution) �i�S��*%��x
��ϋ�c�w�`�1Ί������� /FirstChar 33 endobj endobj 188 0 obj endobj << endobj /LastChar 196 680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 (Distributions: definition) 80 0 obj 168 0 obj 144 0 obj 120 0 obj 51 0 obj >> endobj 500 500 611.1 500 277.8 833.3 750 833.3 416.7 666.7 666.7 777.8 777.8 444.4 444.4 endobj /D [185 0 R /XYZ 105.869 699.082 null] 175 0 obj 527.8 314.8 524.7 314.8 314.8 524.7 472.2 472.2 524.7 472.2 314.8 472.2 524.7 314.8 X.�� (The heat kernel) 500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000 500 444.4 611.1 777.8 777.8 777.8 777.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 164 0 obj 787 0 0 734.6 629.6 577.2 603.4 905.1 918.2 314.8 341.1 524.7 524.7 524.7 524.7 524.7 0 0 0 0 0 0 0 0 0 0 0 0 675.9 937.5 875 787 750 879.6 812.5 875 812.5 875 0 0 812.5 << /S /GoTo /D (subsection.3.4.3) >> 277.8 500 555.6 444.4 555.6 444.4 305.6 500 555.6 277.8 305.6 527.8 277.8 833.3 555.6 << endobj endobj 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 627.2 817.8 766.7 692.2 664.4 743.3 715.6 31 0 obj endobj endobj /Subtype/Type1 /Name/F6 endobj endobj endobj << /S /GoTo /D (section.5.3) >> << /S /GoTo /D (subsection.2.2.1) >> endobj 171 0 obj endobj >> 63 0 obj /Type/Font /LastChar 196 endobj (The zeta function, primes and Dirichlet's theorem) endobj << /S /GoTo /D (section.3.6) >> << 60 0 obj (The Fourier transform) 32 0 obj << 104 0 obj /Widths[314.8 527.8 839.5 786.1 839.5 787 314.8 419.8 419.8 524.7 787 314.8 367.3 << /S /GoTo /D (subsection.3.4.2) >> << /S /GoTo /D (chapter.6) >> xڅ��j�0E���YJO���]�)Z << /S /GoTo /D (chapter.2) >> endobj endobj endobj endobj 500 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 625 833.3 /Length 2502 << /S /GoTo /D (subsection.4.2.2) >> << /S /GoTo /D (section.3.5) >> (The derivative of a distribution) /Type /Page 56 0 obj 152 0 obj endobj /Type/Font /Length 1156 687.5 312.5 581 312.5 562.5 312.5 312.5 546.9 625 500 625 513.3 343.8 562.5 625 312.5 675.9 1067.1 879.6 844.9 768.5 844.9 839.1 625 782.4 864.6 849.5 1162 849.5 849.5 (The wave equation in d=2) 643.8 920.4 763 787 696.3 787 748.8 577.2 734.6 763 763 1025.3 763 763 629.6 314.8 36 0 obj endstream endobj 71 0 obj (Fourier series) << /S /GoTo /D (section.6.1) >> << /D [185 0 R /XYZ 106.869 668.127 null] endobj (Introduction) 163 0 obj 48 0 obj endobj 132 0 obj endobj /Contents 187 0 R 777.8 777.8 1000 1000 777.8 777.8 1000 777.8] q�t�&J"��JK���E%���h4��Ab���Go��j)�� 44 0 obj stream endobj 306.7 766.7 511.1 511.1 766.7 743.3 703.9 715.6 755 678.3 652.8 773.6 743.3 385.6 167 0 obj endobj >> /Font << /F30 190 0 R /F31 191 0 R >> 123 0 obj /Name/F1 endobj /BaseFont/UZRCXL+CMTI10 160 0 obj endobj 8 0 obj /Type/Font /ProcSet [ /PDF /Text ] t��YOMM N#�)7u��!�A�=�y=�7"W�#��}VL��Ii�<5c=��80�q���Y/iF��}�V}���e��Wn�9���`O&�5Z]�
pf�#�DИ�(銾'h� 4��:��F� w#Ŏ�"rRD�$I��3��d�g�S���M�j�I��}3�`gj3��� GA�_��. endobj stream << 83 0 obj /FontDescriptor 14 0 R << /S /GoTo /D (section.5.4) >> �7�A���H�i.� 7]s8MnJ����ikNV��]�&�����h��a4. << /S /GoTo /D (subsection.4.3.1) >> endobj << /S /GoTo /D (subsection.2.3.1) >> 285.5 799.4 485.3 485.3 799.4 770.7 727.9 742.3 785 699.4 670.8 806.5 770.7 371 528.1 endobj 277.8 305.6 500 500 500 500 500 750 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 stream 176 0 obj << endobj 159 0 obj 28 0 obj 743.3 743.3 613.3 306.7 514.4 306.7 511.1 306.7 306.7 511.1 460 460 511.1 460 306.7 << /S /GoTo /D (section.6.3) >> � �|�?�w�+C�����BZ8�2 ^U��tԴ$�����`��O_�EjuyX��Sjh`� )�2�_���yhd~T]���f6�+�2�\*����^�}h��&q������^��]F���yoN��G?4�'�v���A��cx���}��p /Font << /F8 197 0 R >> 21 0 obj W+�╊�X?DA�i�IO9q>&@�Ò�hT�L�vhF��.�}r�ۤύ�۶�n=��B\8�q��5��ֹ�����h�8��B��/�'^��_��=�CZ0��n���h��\T�D��+;x�&i>�Қr���V�Pg��q� << /S /GoTo /D (subsection.2.1.1) >> endobj << /S /GoTo /D (section.2.1) >> 513.9 770.7 456.8 513.9 742.3 799.4 513.9 927.8 1042 799.4 285.5 513.9] /Contents 195 0 R (The functional equation for the zeta function) 277.8 500] endobj endobj /Widths[1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 9 0 obj 108 0 obj endobj << /S /GoTo /D (section.5.2) >> /Subtype/Type1 endobj << /S /GoTo /D (section.4.2) >> endobj << /S /GoTo /D (section.3.3) >> 40 0 obj /Parent 192 0 R /BaseFont/RSIIJF+CMR9 140 0 obj (The Riemann zeta function) endobj 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 endobj 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 642.3 856.5 799.4 713.6 685.2 770.7 742.3 799.4 (The wave equation in d=3) << /S /GoTo /D (section.3.7) >> %PDF-1.5 314.8 787 524.7 524.7 787 763 722.5 734.6 775 696.3 670.1 794.1 763 395.7 538.9 789.2 (The transpose of a linear transformation) 16 0 obj endobj
.
Alex Kidd In The Enchanted Castle Rom,
Pj Ppcocaine Age,
How To Can Diced Tomatoes Without A Canner,
Ktm 390 Adventure Specs,
Are Humans Monogamous Or Polygamous?,
Good Catch Tuna,
Cuisinart Green Gourmet Gg22-20,
Sunday School Lesson On Spiritual Warfare,
Verseview Bible Apk,
Best Strat Tremolo Bridge Replacement,