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Package hyperref Info: Link coloring OFF on input line 22. (/usr/share/texmf-tetex/tex/latex/hyperref/nameref.sty Package: nameref 2003/12/03 v2.21 Cross-referencing by name of section \c@section@level=\count110 ) LaTeX Info: Redefining \ref on input line 22. LaTeX Info: Redefining \pageref on input line 22. LaTeX Font Info: Try loading font information for U+msa on input line 24. (/usr/share/texmf-tetex/tex/latex/amsfonts/umsa.fd File: umsa.fd 2002/01/19 v2.2g AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 24. (/usr/share/texmf-tetex/tex/latex/amsfonts/umsb.fd File: umsb.fd 2002/01/19 v2.2g AMS font definitions ) [1 ] [1] (./current.toc [1 ] LaTeX Font Info: Try loading font information for OT2+wncyr on input line 42 . (/usr/share/texmf-tetex/tex/latex/cyrillic/ot2wncyr.fd File: ot2wncyr.fd 1999/12/17 v3.2a Computer Modern Cyrillic font definitions )) \tf@toc=\write3 \openout3 = `current.toc'. [2] Chapter 1. Overfull \hbox (15.05627pt too wide) in paragraph at lines 96--100 \OT1/cmr/m/n/10 theorem to obtain density result about irreducibility of the ch aracteristic polynomial [] Overfull \hbox (1.09085pt too wide) in paragraph at lines 96--100 \OT1/cmr/m/n/10 of the Hecke operators attached to the weight 24 cusp forms of level 1, $[]\OML/cmm/m/it/10 S[]\OT1/cmr/m/n/10 (^^@[](1))\OML/cmm/m/it/10 :$ [] [3 ] Overfull \hbox (11.11288pt too wide) in paragraph at lines 113--118 \OT1/cmr/bx/n/10 Theorem 1.1.2 \OT1/cmr/m/n/10 (Chebotarev Density Theorem)\OT1 /cmr/bx/n/10 . [][]\OT1/cmr/m/it/10 Let $\OML/cmm/m/it/10 L$ \OT1/cmr/m/it/10 b e a finite Galois extension [] Overfull \hbox (1.4766pt too wide) in paragraph at lines 113--118 \OT1/cmr/m/it/10 of the number field $\OML/cmm/m/it/10 K$\OT1/cmr/m/it/10 , wit h $[][]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 L=F\OT1/cmr/m/n/10 ) = \OML/cmm/m/it/1 0 G:$ \OT1/cmr/m/it/10 Let $\OML/cmm/m/it/10 X \OMS/cmsy/m/n/10 ^^Z \OML/cmm/m/ it/10 G$\OT1/cmr/m/it/10 , stable under conjugation. [] [4] Overfull \hbox (7.77362pt too wide) in paragraph at lines 184--187 [][][]\OT1/cmr/m/n/10 Now let $\OML/cmm/m/it/10 G \OT1/cmr/m/n/10 = []([][]\OML /cmm/m/it/10 =\U/msb/m/n/10 Q\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 ;$ \OT1/cmr/m/n/ 10 then $[]\OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 G\OMS/cmsy/m/n/10 j \OT1/cmr/m/n/ 10 = \OMS/cmsy/m/n/10 j []\OT1/cmr/m/n/10 ([]([]))\OMS/cmsy/m/n/10 j \OT1/cmr/m /n/10 = \OMS/cmsy/m/n/10 j [][]\OT1/cmr/m/n/10 (\U/msb/m/n/10 F[]\OT1/cmr/m/n/1 0 )\OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 ;$ [] Overfull \hbox (5.71777pt too wide) in paragraph at lines 188--192 \OT1/cmr/m/n/10 for each conjugacy class $[]\OML/cmm/m/it/10 c \OMS/cmsy/m/n/10 2 [][]\OT1/cmr/m/n/10 (\U/msb/m/n/10 F[]\OT1/cmr/m/n/10 )$ whose trace is in $ []\U/msb/m/n/10 F[]\OML/cmm/m/it/10 :$ \OT1/cmr/m/n/10 Here, $[[]([]([][]))]$ [] [5] Overfull \hbox (2.61983pt too wide) detected at line 248 \OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 p \OT1/cmr/m/n/10 : [](\OML/cmm/m/it/10 T[]\ OT1/cmr/m/n/10 )[]\U/msb/m/n/10 Q\OMS/cmsy/m/n/10 g ^^Z f\OML/cmm/m/it/10 p \OT 1/cmr/m/n/10 : [](\OML/cmm/m/it/10 T[]\OT1/cmr/m/n/10 )[]\U/msb/m/n/10 F[]\OMS/ cmsy/m/n/10 g\OML/cmm/m/it/10 : [] Overfull \hbox (4.27536pt too wide) in paragraph at lines 248--250 []\OT1/cmr/m/n/10 We have the density of $[]\OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 p \OT1/cmr/m/n/10 : [](\OML/cmm/m/it/10 T[]\OT1/cmr/m/n/10 )[]\U/msb/m/n/10 Q\O MS/cmsy/m/n/10 g \OT1/cmr/m/n/10 = 0\OML/cmm/m/it/10 :$ \OT1/cmr/m/n/10 This co ncludes [] Overfull \hbox (21.33401pt too wide) in paragraph at lines 278--283 [][]\OT1/cmr/m/n/10 Farmer and James (see [[]] and [[]]) verified that the char acteristic polynomials [] Overfull \hbox (0.71542pt too wide) in paragraph at lines 284--287 \OT1/cmr/bx/n/10 Problem 1.3.1. [][]\OT1/cmr/m/n/10 Greatly extend the range of computation carried out by Farmer [] [6] Chapter 2. Overfull \hbox (13.20847pt too wide) in paragraph at lines 321--326 \OT1/cmr/bx/n/10 Remark 2.1.2. [][]\OT1/cmr/m/n/10 (From Richard Taylor) Proble m []2.1.1[] seems to me straightforward. [] [7 ] Overfull \hbox (10.95418pt too wide) in paragraph at lines 340--340 [][]\OT1/cmr/bx/n/14.4 Non-liftable weight one modular forms over $\U/msb/m/n/1 4.4 F[]$ [] Overfull \hbox (19.41728pt too wide) in paragraph at lines 343--354 [][][]\OT1/cmr/m/n/10 This problem is closely connected to the "big images" cha llenge, and could/should [] Overfull \hbox (1.66928pt too wide) in paragraph at lines 343--354 \OT1/cmr/m/n/10 be treated in collaboration. Modular forms of weight 1 over $[] \U/msb/m/n/10 F[]$ \OT1/cmr/m/n/10 behave completely [] [8] Chapter 3. [9 ] Chapter 4. [10 ] [11] Overfull \hbox (12.9636pt too wide) in paragraph at lines 507--511 [][]\OT1/cmr/m/n/10 contains a ``substantial chunk'' of the curves of conductor $\OMS/cmsy/m/n/10 ^^T \OT1/cmr/m/n/10 234446$. Challenge []4.2.1[] [] [12] Overfull \hbox (0.41504pt too wide) in paragraph at lines 594--597 \OT1/cmr/m/n/10 tables that are easy to use in \OT1/cmss/m/n/10 SAGE\OT1/cmr/m/ n/10 . (I think I have an implementation somewhere [] [13] Chapter 5. [14 ] [15] Chapter 6. [16 ] Overfull \hbox (24.72937pt too wide) in paragraph at lines 717--719 \OT1/cmr/bx/n/10 Problem 6.1.1. [][]\OT1/cmr/m/n/10 Implement the full algorith m in \OT1/cmss/m/n/10 SAGE\OT1/cmr/m/n/10 . (It is completely implemented [] [17] [18] Underfull \hbox (badness 2401) in paragraph at lines 907--907 [][][][]\OT1/cmr/m/n/8 Kedlaya's algorithm only requires good reduction; howeve r, the application to [] [19] Overfull \hbox (1.50313pt too wide) in paragraph at lines 931--932 []\OT1/cmr/m/n/10 denote the coordinate ring of $[]\OML/cmm/m/it/10 C[]$ \OT1/c mr/m/n/10 over $[]\U/msb/m/n/10 Q[]$\OT1/cmr/m/n/10 . Recall that the hyperelli ptic involution [] [20] [21] Overfull \hbox (3.36763pt too wide) in paragraph at lines 1013--1015 \OT1/cmr/bx/n/10 Problem 6.2.3. [][]\OT1/cmr/m/n/10 Implement a \OT1/cmr/m/it/1 0 highly optimized \OT1/cmr/m/n/10 version of the reduction algorithm [] Overfull \hbox (59.569pt too wide) in paragraph at lines 1039--1039 [] [] [22] Overfull \hbox (12.1358pt too wide) detected at line 1079 \OML/cmm/m/it/10 F[] \OMS/cmsy/m/n/10 ^^Q \OT1/cmr/m/n/10 (10 + 10\OML/cmm/m/it /10 x \OT1/cmr/m/n/10 + 5\OML/cmm/m/it/10 x[] \OT1/cmr/m/n/10 + (20 + 5\OML/cmm /m/it/10 x \OT1/cmr/m/n/10 + 15\OML/cmm/m/it/10 x[]\OT1/cmr/m/n/10 )\OML/cmm/m/ it/10 z[] \OT1/cmr/m/n/10 + (10 + 20\OML/cmm/m/it/10 x \OT1/cmr/m/n/10 + 15\OML /cmm/m/it/10 x[]\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 z[]\OT1/cmr/m/n/10 )\OML/cmm/ m/it/10 zdx\OT1/cmr/m/n/10 ([]25)\OML/cmm/m/it/10 : [] Overfull \hbox (55.16774pt too wide) detected at line 1088 \OT1/cmr/m/n/10 (13 + 2\OML/cmm/m/it/10 x \OT1/cmr/m/n/10 + 13\OML/cmm/m/it/10 z[] \OT1/cmr/m/n/10 + 10\OML/cmm/m/it/10 z[]x \OT1/cmr/m/n/10 + 7\OML/cmm/m/it/ 10 z[]x[] \OT1/cmr/m/n/10 + 10\OML/cmm/m/it/10 z[] \OT1/cmr/m/n/10 + 20\OML/cmm /m/it/10 z[]x \OT1/cmr/m/n/10 + 15\OML/cmm/m/it/10 z[]x[]\OT1/cmr/m/n/10 )\OML/ cmm/m/it/10 zdx \OMS/cmsy/m/n/10 ^^@ \OT1/cmr/m/n/10 10\OML/cmm/m/it/10 d\OT1/c mr/m/n/10 (\OML/cmm/m/it/10 z[]\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ \OT1/cmr/ m/n/10 15\OML/cmm/m/it/10 d\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 xz[]\OT1/cmr/m/n/1 0 ) \OMS/cmsy/m/n/10 ^^@ \OT1/cmr/m/n/10 5\OML/cmm/m/it/10 d\OT1/cmr/m/n/10 (\O ML/cmm/m/it/10 x[]z[]\OT1/cmr/m/n/10 ) [] [23] Overfull \hbox (69.74638pt too wide) in paragraph at lines 1200--1200 [] \OT1/cmtt/m/n/10 b = binomial(-1/2, k) * p^(k+1) * G^k * x^(p*(i+1)-1 ) * z^((2*k+1)*p-1)[] [] [24] Overfull \hbox (80.24629pt too wide) in paragraph at lines 1200--1200 [] \OT1/cmtt/m/n/10 for i in range(3) for j in ran ge(1,5 +1) if j%2!=0][] [] Overfull \hbox (106.49606pt too wide) in paragraph at lines 1200--1200 [] \OT1/cmtt/m/n/10 H1 = [coefficient_vector(reduce_mod(S(1),5)), coefficien t_vector(reduce_mod(x,5))][] [] Overfull \hbox (1.49698pt too wide) in paragraph at lines 1200--1200 [] \OT1/cmtt/m/n/10 if f is a polynomial in n variables and z is the var_num ber-th[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 1200--1200 [] \OT1/cmtt/m/n/10 generator of the parent of f, this returns the degree-d list of[] [] Overfull \hbox (6.74693pt too wide) in paragraph at lines 1200--1200 [] \OT1/cmtt/m/n/10 Return the 3x3 matrix mod p of coefficients of the coeff icients[] [] [25] Overfull \hbox (48.74657pt too wide) in paragraph at lines 1200--1200 []\OT1/cmtt/m/n/10 find_lincomb_needed_to_subtract_off(reduce_mod((1/5)*(10*z^2 +5*z^2*x),5),2)[] [] Overfull \hbox (111.74602pt too wide) in paragraph at lines 1200--1200 []\OT1/cmtt/m/n/10 find_lincomb_needed_to_subtract_off(reduce_mod((1/5)*(10*z^4 +20*z^4*x+15*z^4*x^2),5),4)[] [] Overfull \hbox (2.75708pt too wide) in paragraph at lines 1205--1210 \OT1/cmr/bx/n/10 Problem 6.2.4. [][]\OT1/cmr/m/n/10 Are there simplifications o ne could make to the above algorithm [] [26] Overfull \hbox (10.49779pt too wide) in paragraph at lines 1247--1255 \OT1/cmr/bx/n/10 Problem 6.2.9. [][]\OT1/cmr/m/n/10 (From Christian Wuthrich.) There is a well-defined supersingular [] Overfull \hbox (0.90805pt too wide) in paragraph at lines 1247--1255 \OT1/cmr/m/n/10 theory explained by Perrin-Riou. The Kedlaya algorithm can be u sed to compute [] [27] Chapter 7. Overfull \hbox (13.02846pt too wide) in paragraph at lines 1287--1292 [][][]\OT1/cmr/m/n/10 Unfortunately, it seems that nobody has proved or even fo rmulated a conjectural [] Overfull \hbox (1.19853pt too wide) in paragraph at lines 1287--1292 \OT1/cmr/m/n/10 is work about higher congruences in that comes up when studying $[]\OML/cmm/m/it/10 p$\OT1/cmr/m/n/10 -adic modular [] [28 ] [29] Chapter 8. [30 ] Overfull \hbox (2.28296pt too wide) in paragraph at lines 1428--1433 \OT1/cmr/m/n/10 preference for $[][]$ or $[]$ to have the larger endomorphism r ing. Can one determine [] Overfull \hbox (15.5771pt too wide) in paragraph at lines 1434--1436 [][][]\OT1/cmr/m/n/10 Note that the condition $[\OMS/cmsy/m/n/10 O[] \OT1/cmr/m /n/10 : \U/msb/m/n/10 Z\OT1/cmr/m/n/10 [\OML/cmm/m/it/10 ^^Y[]\OT1/cmr/m/n/10 ] ] \OMS/cmsy/m/n/10 ^^Q \OT1/cmr/m/n/10 0 [] 5$ is equivalent, up to isomorphi sm, [] [31] Overfull \hbox (11.44513pt too wide) in paragraph at lines 1488--1491 [][]\OT1/cmr/m/n/10 The problem of computing $[](\OML/cmm/m/it/10 A=\U/msb/m/n/ 10 Q\OT1/cmr/m/n/10 )$ has been solved by Stein (and is implemented [] [32] Overfull \hbox (0.88469pt too wide) in paragraph at lines 1548--1548 [][]\OT1/cmr/bx/n/14.4 Mordell-Weil Groups and Torsion subgroups [] [33] Overfull \hbox (1.49698pt too wide) in paragraph at lines 1617--1617 [][][] \OT1/cmtt/m/n/10 [ ] [10] MR1300880 (95h:11053) Flach, Matthias On the degree of[] [] Overfull \hbox (17.24684pt too wide) in paragraph at lines 1617--1617 [] \OT1/cmtt/m/n/10 modular parametrizations. Seminaire de Theorie des Nombre s, Paris,[] [] Overfull \hbox (27.74675pt too wide) in paragraph at lines 1617--1617 [] \OT1/cmtt/m/n/10 1991--92, 23--36, Progr. Math., 116, Birkhaeuser Boston, Boston, MA,[] [] [34] [35] [36] Overfull \hbox (17.01404pt too wide) in paragraph at lines 1800--1807 \OT1/cmr/bx/n/10 Remark 8.8.8. [][]\OT1/cmr/m/n/10 The work of Cristian Wuthric h and Stein mentioned in Section []8.8.1[] [] :<+ current.bbl (./current.bbl [37] Underfull \hbox (badness 10000) in paragraph at lines 11--14 [][][]\OT1/cmr/m/n/10 A. Agashe, K.A. Ribet, and W.A. Stein, [] Underfull \hbox (badness 10000) in paragraph at lines 11--14 \OT1/cmr/m/it/10 The Manin Constant\OT1/cmr/m/n/10 , JPAM Coates Volume, [] Underfull \hbox (badness 10000) in paragraph at lines 11--14 \OT1/cmtt/m/n/10 http://modular.math.washington.edu/papers/ars-manin/ [] Underfull \hbox (badness 1616) in paragraph at lines 16--20 [][][]\OT1/cmr/m/n/10 A. Agashe and W. Stein, \OT1/cmr/m/it/10 Visible evidence for the Birch and [] Underfull \hbox (badness 2922) in paragraph at lines 52--56 [][][]\OT1/cmr/m/n/10 B. Edixhoven, \OT1/cmr/m/it/10 Point counting after Kedla ya, EIDMA-Stieltjes [] Overfull \hbox (113.55426pt too wide) in paragraph at lines 52--56 \OT1/cmtt/m/n/10 http://www.math.leidenuniv.nl/ edix/oww/mathofcrypt/carls[]edi xhoven/kedlaya.pdf\OT1/cmr/m/n/10 . [] [38 ] Package amsfonts Warning: Obsolete command \bold; \mathbf should be used instea d on input line 64. Underfull \hbox (badness 1221) in paragraph at lines 63--66 \OT1/cmr/m/n/10 Amer. J. Math. \OT1/cmr/bx/n/10 123 \OT1/cmr/m/n/10 (2001), no. 3, 475--503. MR MR1833149 [] Underfull \hbox (badness 2503) in paragraph at lines 78--81 [][][]\OT1/cmr/m/n/10 K. Kedlaya, \OT1/cmr/m/it/10 Computing zeta functions via $\OML/cmm/m/it/10 p$\OT1/cmr/m/it/10 -adic cohomology\OT1/cmr/m/n/10 , [] Underfull \hbox (badness 2469) in paragraph at lines 118--121 [][][]\OT1/cmr/m/n/10 Bernadette Perrin-Riou, \OT1/cmr/m/it/10 Arithm^^Setique des courbes elliptiques ^^Ra [] [39] Underfull \hbox (badness 1888) in paragraph at lines 128--132 [][][]\OT1/cmr/m/n/10 K.A. Ribet and W.A. Stein, \OT1/cmr/m/it/10 Lectures on S erre's conjectures\OT1/cmr/m/n/10 , [] Underfull \hbox (badness 10000) in paragraph at lines 142--145 [][][]\OT1/cmr/m/n/10 William Stein and David Joyner, \OT1/cmr/m/it/10 Sage: Sy stem for [] Underfull \hbox (badness 10000) in paragraph at lines 142--145 \OT1/cmr/m/it/10 algebra and geometry experimentation\OT1/cmr/m/n/10 , Communic ations in [] Underfull \hbox (badness 1253) in paragraph at lines 142--145 \OT1/cmr/m/n/10 Computer Algebra (SIGSAM Bulletin) \OT1/cmr/bx/n/10 39 \OT1/cmr /m/n/10 (June 2005), no. 2, [] ) :<- [40] (./current.aux) ) Here is how much of TeX's memory you used: 3382 strings out of 95332 40993 string characters out of 1187736 90642 words of memory out of 1000000 6436 multiletter control sequences out of 10000+50000 21508 words of font info for 81 fonts, out of 500000 for 2000 0 hyphenation exceptions out of 8191 31i,12n,29p,382b,261s stack positions out of 1500i,500n,5000p,200000b,5000s Output written on current.dvi (42 pages, 158224 bytes).