Veronica arvensis L., Sp. Pl. 1: 13 13 1753. (syn: Agerella arvensis (L.) Fourr.; Cardia arvensis (L.) Dulac; Veronica acinifolia F.W.Schmidt; Veronica arvensis subsp. pennellii Elenevskii; Veronica bellardii All.; Veronica brevi-pedunculata Gilib.; Veronica hawaiensis H.Lév.; Veronica hirsuta Luce; Veronica micrantha Schur; Veronica polyanthos Thuill.; Veronica pseudoarvensis Tineo;Veronica romana F.W.Schmidt);    
  
Albania, Austria, Belgium, Baleares, England, Bulgaria, Corsica, Czech Republic,
Slovakia, Denmark, Finland, France, Germany, Ireland, Switzerland, Netherlands,
Andorra, Spain, Gibraltar, Hungary, Iceland (I), Italy, Serbia & Kosovo,
Montenegro, Macedonia, Slovenia, Croatia, Bosnia & Hercegovina, Portugal,
Malta, Norway, Poland, Romania, Sardinia, Sicily, Sweden, Algeria, Crimea,
Estonia, Latvia, Lithuania, W-, C-, N- & E-European Russia, Belarus,
Ukraine, Northern Caucasus, Armenia, Azerbaijan, Georgia [Caucasus], Russian Far
East (I), Turkey (Inner Anatolia, N-Anatolia, NE-Anatolia, NW-Anatolia:
Bithynia, S-Anatolia, SE-Anatolia: Mesopotamian Anatolia, SSW-Anatolia,
SW-Anatolia, W-Anatolia), Cyprus (C-Mountains, N-Cyprus, W-Cyprus), Greece
(incl. Kiklades), Crete, East Aegaean Isl., Rhodos, European Turkey, Iran
(EC-Iran, N-Iran), Iraq (NE-Iraq), Israel (coastal W-Israel, Rift Valley,
N-Israel), Lebanon (Antilebanon, C-Lebanon, coastal W-Lebanon), Syria (C-Syrian
Desert, NW-Syria, Jbel Druze, W-Syrian Mountains), Afghanistan (Kunar /
Nuristan, Takhar), Azores (Santa Maria Isl., Sao Miguel Isl., Terceira,
Graciosa, Sao Jorge, Pico, Faial, Flores Isl., Corvo Isl.), Madeira (Madeira
Isl., Porto Santo Isl.), Canary Isl. (Lanzarote, Fuerteventura, Gran Canaria,
Tenerife, La Gomera, Hierro, La Palma), Kazakhstan, Kyrgyzstan, Tajikistan,
Uzbekistan, Pakistan (Swat, Hazara), Jammu & Kashmir (Kashmir, Jammu,
Poonch), Sri Lanka, S-India,
Turkmenistan, Ethiopia, Costa Rica (I), Panama (I),
Haiti (I), Dominican Republic (I), Bermuda (I), Australia (I) (Western Australia
(I), South Australia (I), Queensland (I), New South Wales (I), Victoria (I),
Tasmania (I)), Taiwan (I), Auckland Isl. (I), Jamaica (I), Peru (I), South
Africa (I), New Zealand (I), Chatham Isl. (I), Lord Howe Isl. (I), Norfolk Isl.
(I), China (I) (Anhui (I), Fujian (I), Henan (I), Hubei (I), Hunan (I), Jiangsu
(I), Jiangxi (I), Shandong (I)), Korea (I), Taiwan (I), trop. Africa (I),
Madagascar (I), Ecuador (I), Mexico (I), Guatemala (I), Chile (I), Juan Fdz.
Isl. (I), Argentina (I), Uruguay (I), Brazil (I), Bolivia (I), Colombia (I), La
Runion (I), Hawaii (I) (Molokai (I), Maui (I), Hawaii Isl. (I)), Alaska (I), USA
(I) (Alabama (I), Arkansas (I), Arizona (I), California (I), Colorado (I),
Connecticut (I), District of Columbia (I), Delaware (I), Florida (I), Georgia
(I), Iowa (I), Idaho (I), Illinois (I), Indiana (I), Kansas (I), Kentucky (I),
Louisiana (I), Massachusetts (I), Maryland (I), Maine (I), Michigan (I),
Minnesota (I), Missouri (I), Mississippi (I), Montana (I), North Carolina (I),
Nebraska (I), New Hampshire (I), New Jersey (I), New Mexico (I), Nevada (I), New
York (I), Ohio (I), Oklahoma (I), Oregon (I), Pennsylvania (I), Rhode Island
(I), South Carolina (I), South Dakota (I), Tennessee (I), Texas (I), Utah (I),
Virginia (I), Vermont (I), Washington State (I), Wisconsin (I), West Virginia
(I), Wyoming (I)), Canada (I) (British Columbia (I), New Brunswick (I),
Newfoundland (I), Nova Scotia (I), Ontario (I), Quebec (I), Yukon (I)),
Greenland (I), St. Pierre et Miquelon (I)
as per Catalogue of life;
Corn Speedwell; 
 
Scrophulariaceae of the Western Himalayas By Francis . Pennell (Description & Keys- Veronica capitata, cachemirica, lanosa, macrostemon, lasiocarpa, serpyllifolia, verna, arvensis, didyma (syn. of Veronica polita Fr. as per The Plant List), persica, perpusilla (syn. of Veronica pusilla Kotschy & Boiss. as per The Plant List), uncinata (syn. of Veronica rubrifolia Boiss. as per The Plant List), biloba, campylopoda, stewartii, koelzii, cephaloides (syn. of Veronica ciliata subsp. cephaloides (Pennell) D.Y. Hong as per The Plant List), hirta, nana (syn. of Veronica ciliata subsp. cephaloides (Pennell) D.Y. Hong as per The Plant List), melissaefolia, javanica, cana, umbelliformis (syn. of Veronica szechuanica subsp. sikkimensis (Hook. f.) D.Y. Hong as per The Plnat List), beccabunga, anagallis-aquatica, secunda, salina & undulata)
 


The species (Veronica didyma syn. of Veronica polita ) is quite distinct from V. persica in smaller pinkish flowers, pedicels shorter than subtending leaves (bracts), broadly triangular ovate leaves (usually broader than long), capsule with rounded lobes, diverging at acute angle or almost subparallel, covered with longer glandular hairs mixed with shorter simpler hairs, broader calyx lobes overlapping at base.
European V. agrestis L. has ovate leaves, longer than width, fruit covered with only glandular hairs and shorter style. 

V. persica, though closer to V. didyma is much different in leaf shape and size, length of pedicel and fruit, which has a widely diverging sinus (obtuse angle) and keeled lobes in fruit. Flower is also larger.
V. arvensis, though having similar leaves is much different with subtending bracts much smaller than foliage leaves and aggregated in terminal inflorescence. also the pedicels are much smaller


 

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Veronica arvensis Linnaeus, Sp. Pl. 1: 13. 1753.

Erect or ascending annual herb with multicellular hairs in two lines; leaves in 3-5 pairs, ovate-orbicular, up to 15 mm long, lower short petiolate, upper sessile; flowers in terminal racemes elongated in fruit; calyx 4-lobed, 3-4 mm long; corolla blue, shorter than calyx with orbicular to oblong lobes; capsule obcordate, strongly compressed, about 3 mm long, margin glandular ciliate, notch deep, lobes rounded, style shorter than or equalling lobes.

Common weed in Kashmir valley in fields and roadsides, photographed from Avantipore in Kashmir.


Veronica arvensis Linnaeus, Sp. Pl. 1: 13. 1753.  
Erect or ascending annual herb with multicellular hairs in two lines; leaves in 3-5 pairs, ovate-orbicular, up to 15 mm long, lower short petiolate, upper sessile; flowers in terminal racemes elongated in fruit; calyx 4-lobed, 3-4 mm long; corolla blue, shorter than calyx with orbicular to oblong lobes; capsule obcordate, strongly compressed, about 3 mm long, margin glandular ciliate, notch deep, lobes rounded, style shorter than or equalling lobes.
Common weed in Kashmir valley in fields and roadsides, photographed from Avantipore in Kashmir.


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Veronica arvensis 

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Herb from Nilgiris for id 160211MK2: (Mixed thread): 3 correct images as above.
……………….

You have what looks to be V. arvensis mixed – notice the small very short-stalked flowers and the upper flower leaves are like tongues  –
Image 3


  

 
References: